Introduction

Habitat loss and fragmentation have been recognized as two major threats to the viability of animal species and have become a major subject of research in ecology (Wilcox and Murphy 1985; Forman 1996; Villard 2002; Fahrig 2003). Habitat loss results in heterogeneous landscapes often composed of isolated patches of suitable habitat which are embedded within a matrix of varying quality. One of the most pressing ecological questions arising is how to manage such landscape mosaics for species conservation (Fahrig 2003), and whether it is better to extend existing habitat patches or create further patches within the landscape (Sutherland et al. 2006). Connectivity of a landscape is important because it may allow exchange of individuals among habitat patches and can counteract stochastic local extinction and has therefore important consequences at the population level (Hanski 1994; Wiegand et al. 1999; Tischendorf and Fahrig 2000b). Structural connectivity is only based on the physical arrangement of the landscape elements (i.e., landscape structure), whereas functional connectivity is based on the behavioural response of organisms to landscape structure (Taylor et al. 2006). A good understanding of the interplay between landscape structure and interpatch movement on population dynamics, i.e. functional connectivity, is crucial for focussing conservation efforts (Bowne and Bowers 2004; Vogt et al. 2009).

Creation of corridors, i.e. linear strips of habitat, and stepping stones, i.e. discontinuous small patches that connect otherwise isolated patches, have been proposed as management strategies to increase structural connectivity in fragmented landscapes (Wilson and Willis 1975; Simberloff et al. 1992; Beier and Noss 1998; Schultz 1998; Jepsen et al. 2005; Chetkiewicz et al. 2006). However, stepping stones received much less attention than corridors (Hobbs 1992; Baum et al. 2004; Uezu et al. 2008), and it is not clear under which circumstances they may enhance functional connectivity and population viability. The general notion is that stepping stones enhance connectivity (Gilpin 1980; Fischer and Lindenmayer 2002). For example, Söndgerath and Schröder (2002) investigated the effects of stepping stones in a mosaic of different habitat suitability for a fictive grasshopper species and found that stepping stone patches greatly increased dispersal for species with limited dispersal ability living in landscapes with isolated habitat patches. However, results of an experimental study by Baum et al. (2004) showed that the effect of stepping stones depended strongly on the composition of the surrounding matrix, with stepping stones failing to improve connectivity in a high-resistance matrix. Uezu et al. (2008) suggest that the efficiency of stepping stones would be optimal at intermediate degrees of matrix resistance.

Most theoretical studies guided by the metapopulation framework assume that a landscape consists of patches of suitable habitat within a ‘matrix’ of unsuitable habitat, but variations in matrix quality can have a wide range of effects on functional connectivity because different matrix types may contribute to patch isolation in nontrivial ways (e.g., Fahrig 2002; Goodwin and Fahrig 2002; Revilla et al. 2004; Wiegand et al. 2005). In the simplest case, as e.g., for the Iberian lynx (Lynx pardinus), dispersing animals may distinguish between preferred dispersal habitat (habitat unsuitable for breeding but which offers cover and resources during dispersal) and actively avoided habitat (Revilla et al. 2004; Revilla and Wiegand 2008). It is therefore important to study the effect of stepping stones within the context of matrix heterogeneity (Fahrig 2007).

Apart from the underlying landscape structure, demographic traits of the species are important for predicting the success of a certain conservation measure like creating stepping stones (Bevers and Flather 1999; Vance et al. 2003; Revilla and Wiegand 2008). In particular, species of conservation concern often suffer from high mortality rates, are poor breeders, and/or occur at low numbers, e.g. after a reintroduction (Wiegand et al. 2004b; Hurford et al. 2006). Low recruitment could lead to a negative effect of stepping-stones in an otherwise connected world. For example, stepping stones could attract the few dispersing individuals and lead to ‘shading effects’ (Hein et al. 2004), because the animals settle in the stepping stone but do not produce enough dispersers to reach the next large population. Nearby stepping stones may also participate in ‘competition between patches’ (Heinz et al. 2005, 2006) and catch dispersers that otherwise may have reached larger patches. In this sense, the putative stepping stones could turn into ‘attractive sinks’ (Delibes et al. 2001).

The above considerations suggest that a systematic analysis of stepping stone effects requires a modelling approach that is able to incorporate realism in demography, dispersal behaviour, and landscape structure to capture the delicate balance among potentially counteracting effects. Individual-based and spatially explicit population models (Wiegand et al. 2004a; Kramer-Schadt et al. 2005) that are optimized using the pattern-oriented modelling strategy (Wiegand et al. 2003; Grimm et al. 2005; Kramer-Schadt et al. 2007) are ideally suited for this purpose. Here, we use such a model developed for the Eurasian lynx (Lynx lynx) and combine it with a neutral landscape approach (Gardner et al. 1987) to systematically explore the effects of stepping stones on functional connectivity. More specifically, we construct landscapes composed of two large breeding habitat patches where only one is initially occupied and produces dispersers which may or may not colonize the second patch. We systematically change the landscape structure of the ‘matrix habitat’ in between the two large patches of breeding habitat, first by placing stepping stones of different number and size and second by changing the proportion and physiognomy of dispersal habitat and avoided habitat.

We selected the Eurasian lynx as study species because stepping stones may have important and direct implications for lynx management as its reintroduction has been conducted or is planned in many European countries (Breitenmoser et al. 2001). In this context, large ‘habitat corridors’ containing stepping stones as mitigation measures for habitat fragmentation enhancing connectivity are planned on a nationwide scale (Boettcher et al. 2005; Reck et al. 2006). Suitable patches could only support small populations of resident individuals due to the lynx’ large home range requirements. Since the nearest other suitable patches or populations may be dozens to hundreds of kilometres away (Schadt et al. 2002a, b), the connectivity between these patches is of paramount importance for the future development and survival of the lynx in human-dominated landscapes.

Methods

To address our objectives we used a spatially explicit population model (Kramer-Schadt et al. 2005), originally developed to evaluate the viability of Eurasian lynx in different habitat patches in Germany. The model incorporates a detailed dispersal model (Kramer-Schadt et al. 2004) that describes the movement of individual lynx within a heterogeneous landscape comprising breeding habitat, dispersal habitat, avoided habitat (but sometimes used), and movement barriers (see also below ‘Landscape maps’). Both the dispersal and population model have been calibrated with field data and contain biological realism in the parameters as well as in the processes (Kramer-Schadt et al. 2007). In the following we provide a brief summary of the model rules, details are provided in the online Supplementary Material.

Lynx dispersal model

The dispersal model (Kramer-Schadt et al. 2004) was parameterized and calibrated with telemetric data from the Swiss Jura collected from 1988 to 1991 (Breitenmoser et al. 2001). The accuracy of the telemetric location data was 1 km², which determined the spatial grain of the model and of the landscapes. Single landscapes are represented as a grid of 1 km2 cells that can be breeding habitat, dispersal habitat, or avoided habitat. The rate at which lynx successfully move among patches emerges from the spatial distribution of habitat types and the individuals’ adaptive traits for dispersal.

The movement path consists of a series of discrete steps to adjacent cells. Every day a disperser decides how many steps (s; in km units) to take during this day. This rule is governed by a probability distribution leading to day-to-day variability in distance moved as observed in real lynx:

$$ P\left( s \right) = ( 1- ((s - 1)/(s_{max} - 1)))^{x} $$
(1)

with parameters s_max = 45 km and x = 11. The grid cell the lynx moves into is calculated under the assumption that lynx can always sense the habitat type of the nine grid cells surrounding its present position. The parameter P matrix (=0.03) controls the relative probability of entering dispersal habitat versus avoided habitat. Furthermore, directed movement is modelled with a correlation factor P C (=0.53) that gives the probability that the lynx continues to move in its current direction. Otherwise, a random direction is chosen. However, staying in dispersal habitat has a stronger effect on the choice of a cell than does correlation in movement direction. A rule is added to avoid the unrealistic behaviour that a lynx stays too long within avoided habitat. If a lynx moves for P maxmat (=10) consecutive steps in avoided habitat it returns to the cell where it left dispersal habitat. This rule can be interpreted as a tacit prediction: an unsuccessful explorative excursion into avoided habitat will be aborted, i.e. lynx cannot cross gaps of unsuitable habitat >10 km.

Lynx population model

The demographic model (Kramer-Schadt et al. 2005) distinguishes the sex of the individual, because males have larger home ranges and different searching strategies. A set of rules assigns each individual one of two possible statuses with different levels of mortality: residents (mortality probability P MR  = 0.1 p.a.) and dispersers (P MD  = 0.0015 p.d.). Only residents can produce offspring, and they can do this only when male and female home ranges are overlapping. Thus, we explicitly consider Allee effects.

At the beginning of each model time step (year) the number of resident males and females and the number of dispersers are determined. All non-residents older than one year disperse and search for home ranges. The decision of whether to establish a home range is determined by a set of rules which take into account local habitat quality. If dispersing females encounter enough empty cells of breeding habitat in their neighbourhood (at least 70–100 cells) or if dispersing males find female home ranges not yet occupied by another male they settle, otherwise they continue dispersal in the next year. Next, for each resident female ≥2 years old and overlapped by a male territory the decision as to whether they reproduce is taken (birth probability P B  = 0.75). In the final step, the demographic variables for each surviving individual (age and status, i.e. disperser or resident) are updated. We assessed model sensitivity by testing different values for disperser mortality P MD (0.0007 p.d.) and birth probability P B (1 p.a.), resulting in four different demographic scenarios. Feedback from habitat quality and density-dependent factors are automatically embedded, since the resident individuals regulate density via their home range size in breeding habitat quality.

Landscape maps

To systematically study the effect of stepping stones we created artificial landscapes which consisted of two large patches of breeding habitat, each 20 km × 65 km in size, that were separated by a 129 km × 65 km wide block. The latter was composed (1) of avoided and dispersal habitat with different composition and degree of fragmentation and (2) different numbers and sizes of stepping stones (=small patches of breeding habitat) (Fig. 1). This design allows for the control of breeding habitat without interfering in the configuration of a realistic landscape. The total size of the landscape was 169 by 65 cells, i.e. ca. 11,000 km2.

Fig. 1
figure 1

Examples of the neutral landscapes with gradients of increasing coverage f D in dispersal habitat (grey; from top to bottom) and contagion (from left to right). Breeding habitat (black) is located on both sides of the map, and the breeding habitat stepping stones are situated in the centre. White areas show avoided habitat. Additionally shown are scenarios with one stepping stone of 500 km², two stepping stones with 200 km² each and four stepping stones with 100 km² each

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Dispersal habitat potentially connecting the two large patches of breeding habitat was created by using the midpoint displacement algorithm by Saupe (1988) described in With (1997). This algorithm allows controlling both dispersal habitat coverage (COV, standing as a synonym for habitat loss) and dispersal habitat contagion (CONT, standing for habitat fragmentation). This algorithm has its basis in fractal geometry and has been found to generate landscapes that strongly resemble real landscapes (Flather and Bevers 2002). Six levels of coverage (10, 20, 30, 40, 60, 80%) and four levels of contagion (randomly distributed to clumped) were used (Fig. 1).

One of the large patches of breeding habitat was the patch of origin holding a persistent lynx population of about 30 residents that continuously produced dispersers. The other large patch was the patch of arrival that initially did not host any lynx but which may be colonized by dispersers from the patch of origin. We selected a distance of 129 km between the two large patches similar to the distance between the Harz Mountains (Germany), which currently hosts a lynx population, and the Thuringian Forest in Germany, an area of lynx conservation concern (Kramer-Schadt et al. 2004).

In between the two breeding patches we placed a variable number of circular stepping stones SSN [none (null model), 1, 2 or 4] of different sizes SSZ (100, 200 or 500 km2), resulting in 10 maps (3 × 3 with stepping stones + 1 null without stepping stones) for each landscape configuration (Fig. 1). The within map size of the stepping stones in those maps containing several stepping stones was constant. As breeding habitat is also used for dispersal by lynx we considered the area of the stepping stones as dispersal habitat when calculating the variable coverage COV that gives the proportion of dispersal habitat in between the two large patches. Thus, certain maps could not be created, because the amount of dispersal habitat after inclusion of large stepping stones would have exceeded the respective COV amount. This was the case for the following 12 maps: COV = 10%, SSZ = 500 km2 and SSN >1 as well as COV = 20%, SSZ = 500 km2 and SSN = 4 for all four values of CONT.

To test for potential shading effects of stepping stones, we created maps that did not contain any dispersal habitat but a 3 km wide corridor connecting the patches of origin and of arrival. Half way down that corridor there was either (a) a breeding habitat patch of 200 km2, or (b) a dispersal habitat patch of the same size or (c) no patch at all while the corridor was widened by the amount of habitat corresponding to the missing patch. In subsequent simulations the breeding habitat patch was also placed at various distances beside the corridor (see insets in Table 2).

Simulation experiments and data analysis

Calculating all sensible combinations of variable landscape parameters resulted in 228 different map types [i.e., (4 levels of contagion × 6 levels of coverage of dispersal habitat) × (10 types of stepping stones) − 12 maps with impossible combinations]. To account for stochastic effects introduced by the midpoint displacement algorithm we created for each of the 24 landscape types (defined by the combination of the coverage and contagion parameters; Fig. 1) 25 different realizations. Population dynamics within every map were repeated 30 times and lasted for 200 years, i.e. for each landscape configuration 25 × 30 = 750 repetitions were run. The sensitivity of the demographic parameters was tested in four different scenarios. Thus, in total we simulated 5700 different landscapes and conducted a total of 5700 × 30 × 4 = 684000 individual simulation runs.

Landscape borders were reflective, characterising ‘real’ landscapes where cities or large agro-ecosystems flank semi-natural habitat, e.g. the Magdeburger Börde or the industrialised and urbanised area along the river Rhine for the case of the lynx in Germany. Initial population size in the patch of origin was 30 individuals (15 females, 15 males). Key parameters of population dynamics within the origin and arrival breeding habitat patches were recorded.

Data analysis focused on the patch of arrival. Because we were interested in how colonization success depends on the structure of dispersal habitat and stepping stones, we used the population growth factor λ (Kramer-Schadt et al. 2005) in the patch of arrival as a dependent variable characterizing the aspects of functional connectivity relevant for our question (Goodwin 2003). As λ measures the success of the entire dispersal and colonization process, it summarizes the combined effects of several factors: the number of dispersers, their individual dispersal success and the establishment of a new viable population that depends on various population dynamical aspects of the lynx and the conditions in the target patch. λ and the proportion of dispersers reaching the target patch may not necessarily be linked, but if λ ≥ 1, then the patch has been reached and colonised successfully.

We first used generalized additive models (GAM; family binomial) to analyze the response of the binary dependent variable ‘successful (λ ≥ 1) and unsuccessful (λ < 1) target patch colonization’ on the independent variables that determined landscape structure and demography. These were dispersal habitat coverage COV, contagion CONT, the number (SSN) and size (SSZ) of stepping stones. Variables with significant non-linear effects (P < 0.05) were modelled as polynomials in the subsequent generalised linear model (GLM). The demographic parameters birth (P B ) and mortality probability (P MD ) were included in the GLM. We analysed main effects as well as two-way interactions. All variables were standardized between 0 and 1 to compare their estimate size. Additionally, variables were ranked using a stepwise backward algorithm based on AIC, i.e. variables with the highest ΔAIC compared to the full model are most significant, since their elimination leads to an increase in the model AIC. To find a hierarchical pattern in the simulated data and to better understand the impact of the different factors (i.e., COV, CONT, SSN, SSZ, P B , P MD ) on the target patch population growth rate λ we conducted a regression tree analysis (De’ath and Fabricius 2000). All analyses were done in R 2.9.2 (http://www.R-project.org).

Results

The GAM analysis revealed that the variables CONT and SSZ did not show linear behaviour (Fig. 2). They were therefore modelled with second-order polynomials in the GLM. The GLM showed that successful colonisation was significantly influenced by all variables, with dispersal habitat coverage COV being the main driver (largest ΔAIC), closely followed by contagion CONT of dispersal habitat and mortality of dispersers P MD (Table 1). An increase in dispersal habitat coverage or decrease in mortality logically enhanced colonization success λ, while an increase in contagion decreased it (Table 1; Fig. 3). The growth rate λ displayed sigmoid behaviour with respect to habitat coverage, with a threshold or critical range at intermediate habitat coverage (Fig. 3). With increasing contagion of dispersal habitat an increasing coverage of dispersal habitat is required for colonization success. In landscapes with randomly distributed dispersal habitat we find that λ > 1 is reached in some cases at 30% of dispersal habitat coverage (Fig. 3a) whereas in clumped landscapes we find λ > 1 at about >60% dispersal habitat coverage (Fig. 3d). This is because clumped landscapes contain large patches of avoided habitat that are insurmountable for the lynx and do not provide connectivity. On the other hand, strongly clumped dispersal habitat can also allow for a successful target patch colonization, provided the coverage of dispersal habitat is sufficiently high (Fig. 4); in this case the large patches of dispersal habitat may coincidently form continuous corridors between the start and target patch.

Fig. 2
figure 2

Results of the binomial GAM dividing the data into successful (λ ≥ 1) and unsuccessful target patch colonisation (λ < 1). The y-axis shows the partials (df = 3 for smoothing function) of the respective variable. The variables contagion of dispersal habitat (CONT) and size of stepping stones (SSZ) do not show linear behaviour and were therefore modelled with second-order polynomials in the GLM (Table 1)

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Table 1 Analysis of parameter estimates of the generalised linear model with binomial error distribution. λ was ≥1 in 404 cases, and <1 in 508 cases (N observations = 912). The variables were standardized to compare their estimates. Variables were ranked using a stepwise backward algorithm based on AIC, i.e. variables with the highest ΔAIC compared to the full model are most significant, since their elimination leads to an increase in the model AIC. Significant variables or interaction terms are marked with a bold P-Value
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Fig. 3
figure 3

The effect of an increase in dispersal habitat coverage on colonisation success λ for the four types of dispersal habitat contagion (a random, b: low, c: medium, d: high contagion) and increasing stepping stone size (dark grey: no stepping stone, grey: 100 km2, lightgrey: 200 km2, white: 500 km2). λ was generally higher in less clumped landscapes. Critical ranges of dispersal habitat coverage where additional factors get decisive for colonisation success lie in the range of 30–60% coverage

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Fig. 4
figure 4

Result of the regression tree analysis. The nodes divide the data into successive clusters with similar characteristics. λ is indicated below each partition of the predictor variable space. The length of the branches gives the relative importance of the variable. (The dotted lines indicate that the length of the variable ‘coverage’ had been shortened for presentation reasons.)

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The regression tree analysis showed a very differentiated and clear picture of the effects of the different variables on colonization success λ (Fig. 4). Overall, this analysis revealed that stepping stones had only a weak effect on colonization success. However, there were significant interactions between number (SSN) and size (SSZ) of stepping stones (Table 1), making them important especially in the critical range of medium dispersal habitat abundance (i.e., COV = 30). Below a threshold of 20% dispersal habitat coverage, the target patch is never successfully colonised (red marked branch of regression tree in Fig. 4). With 30% dispersal habitat coverage demographic parameters become decisive: Under low disperser mortality scenarios, the target patch could still be colonised given random to low dispersal habitat contagion (green branch with COV = 30, P MD low and CONT ≤ 2), whereas under the high dispersal mortality scenario stepping stone size and number must be large to yield positive growth rate λ (blue branch with COV = 30, P MD high, SSZ >200 and SSN >2). Above a threshold of 30% (right branch), the target patch is almost always colonised successfully (i.e., λ ≥ 1). Only when dispersal mortality is high and the size of the stepping stone is small do we get λ < 1 (orange branch with COV = 40, P MD high, SSZ ≤ 200), or when the landscape, i.e. dispersal habitat, is clumped (pink branch with COV = 40, P MD low, CONT >2).

The results for a critical range of dispersal habitat coverage (30%) are shown in more detail in Fig. 5. For less clumped landscapes (Fig. 5a, b) and an optimistic demographic scenario (triangles; high birth rate and low disperser mortality) an increase in stepping stone size and number is positively adding to λ. For less clumped landscapes and the pessimistic demographic scenario colonization is only possible with multiple and large stepping stones (Fig. 5a, b). For clumped landscapes (Fig. 5c, d) colonization success is dramatically reduced in both demographic scenarios and only large numerous stepping stones can counterbalance this trend (big white circles or triangles). With an increase in contagion the standard deviations of λ also increased (results not shown), making colonisation success extremely dependent on how the landscape was clumped, i.e. guiding to the target patch or leading to dead ends. A series of stepping stones in a row may bridge landscapes with large patches of avoided habitat (Fig. 1).

Fig. 5
figure 5

Exploring the critical range of dispersal habitat coverage (COV = 30%) for the four dispersal habitat contagion types (a: random, b: low, c: medium, d: high contagion). Mean λ (y-axis) is shown for two extreme demographic scenarios (triangle: optimistic scenario with high birth rate and low disperser mortality, circles: pessimistic scenario with low birth rate and high disperser mortality) under increasing stepping stone size (x-axis). The grey shade and size code give the number of stepping stones (Black: no stepping stone, grey: one stepping stone, light grey: two stepping stones, white: four stepping stones)

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The decrease of λ in random landscapes with an increase of stepping stone numbers at low coverage of dispersal habitat (Figs. 2, 5a) could be either a shading effect or because the introduction of a stepping stone implies a strong concentration of habitat coverage in that stepping stone. This can produce unbridgeable gaps on the rest of the map. To explore this effect in more detail, simulations where run on maps in which the stepping stones were not introduced as part of the dispersal habitat, but in addition to it (constituting an addition of 1.2% dispersal habitat to the given percentage of dispersal habitat). Colonisation success was higher on landscapes with 10% dispersal habitat plus a stepping stone, i.e. 11.2% dispersal habitat in total, than on 10% dispersal habitat including the stepping stone (i.e. where the amount of habitat needed to create a stepping stone was taken from the 10% dispersal habitat, because stepping stone habitat can also be used for dispersal; Fig. 6, only random landscapes), which is clear from our general result of habitat coverage importance. However, dispersal success on 10% dispersal habitat was even higher when there was no stepping stone at all. Thus, both shading and increased habitat concentration might account for the negative effects of stepping stones at low dispersal habitat coverage.

Fig. 6
figure 6

Investigation of confounding methodological effects when the number of cells that belong to a stepping stone (here, 100 km2) are subtracted from the 10% dispersal habitat coverage (black line) or are added to the 10% dispersal habitat coverage (dotted line) in comparison to a scenario without stepping stones (dashed line)

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Analysing the potential shading effects in the landscapes shown in Table 2 (cf. chapter ‘Landscape Maps’), we found that a corridor connecting the large patches of breeding habitat was more effective when there was a stepping stone (Table 2A, B). There was no shading effect at all. However, if the stepping stone was not assigned a breeding habitat status but only dispersal habitat status, its effect on dispersal success reverses on average to negative (Table 2E), presumably because the bulge in the corridor provided by the non-breeding stepping stone made many lynx leave the corridor. Thus, it can be hypothesized that the positive effect of breeding in a stepping stone can at least partly be counteracted by the shape and location of the stepping stone. This was confirmed by not placing the breeding habitat patch into the corridor, but 2 or 5 km beside the corridor (Table 2C, D). With increasing distance from the corridor the positive effect of the stepping stone declined because individuals that entered the stepping stone did not necessarily manage to get back to the corridor and got trapped. If the stepping stone was 5 km away from the corridor, dispersal success was even lower than when there was a corridor without any stepping stone (Table 2D). This clearly constitutes a shading effect that is caused by a negative effect of landscape configuration exceeding the positive effect of breeding.

Table 2 Different scenarios showing the shading effect of stepping stones in artificial corridor landscapes embedded in avoided habitat
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Discussion

We systematically analysed the effect of varying size (SSZ) and number (SSN) of stepping stones and different levels of dispersal habitat loss (COV) and dispersal habitat fragmentation (CONT) as well as four different demographic scenarios on successful patch colonization for European lynx, a species of conservation concern that occurs at low individual numbers. Such an analysis is especially important, because stepping stones are often considered to be a panacea for connecting and facilitating colonisation of patches that can host only low numbers of a target species. However, our analysis showed that stepping stones had only a weak effect on colonization success and functional connectivity for lynx. Large and/or more numerous stepping stones promoted functional connectivity in cases of intermediate cover of dispersal habitat (30–40%) and high dispersal mortality. Otherwise they can create a variety of contradicting effects on colonization success and may not be per se successful in enhancing functional connectivity for the lynx. An important lesson of our study is that one needs to consider the whole picture including demography before planning conservation actions (Lindenmayer et al. 2008).

We found that the underlying configuration of dispersal habitat has a much stronger effect on connectivity than the stepping stones. This is in line with the empirical findings of Baum et al. (2004). In fact, stepping stones showed negative effects especially at low levels of dispersal habitat coverage, i.e. when a lot of dispersal habitat has already been lost. This is because only few dispersers manage to reach the target patch, and with additional stepping stones these few dispersers get trapped in the stepping stone. Thus, stepping stones in landscapes with low dispersal habitat coverage can act as sinks due to a shading effect (Heinz et al. 2005).

Depending on the landscape configuration, stepping stones often may not be encountered by dispersing individuals. Especially at medium to high contagion we found that adding only few stepping stones had a negative effect on colonization success compared to scenarios without stepping stones. This may firstly be due to large gaps in clumped dispersal habitat that cannot be overcome by dispersers. This negative effect could only be counterbalanced by ‘planning big’, i.e. by placing numerous large stepping stones into the map. Secondly, the underlying configuration of dispersal habitat may not guide the dispersers towards the stepping stone or further towards the target patch as shown with the artificial corridor landscapes (Table 2). Thus, it can be concluded that connectivity is the result of a subtle interplay of dispersal habitat amount, configuration and stepping stones that has to be considered carefully before stepping stones are considered as management measures (see also Wiegand et al. 2005).

However, stepping stones may increase dispersal and colonisation success when they are large enough to host a population which produces dispersing offspring that may colonise the target patch. In contrast, if a stepping stone is too small the newly founded population will go extinct quickly due to chance events, and stepping stones may have a rather negative effect on connectivity. This is because a stepping stone first has to be recolonised again before it can produce dispersers and thus displays a shading effect. The fact, that the number of stepping stones between start and target patch did not have the most significant effect is in line with findings from Hein et al. (2004). Thus, if population connectivity is the primary goal, corridors may serve better.

The assumption of only source, dispersal and avoided habitat is a simplification. For example, Naves et al. (2003) proposed for large carnivores the use of five functional habitat types, and under a broader perspective landscapes have to be considered as dynamic (e.g., Jepsen et al. 2005). However, here we used a functional definition of habitats with respect to use by a specific organism (Wiegand et al. 1999) and not land use or vegetation cover types (Lindenmayer and Fischer 2007). With this perspective the three habitat types are a good approximation within the level of detail of our model.

Stepping stones may have various other positive aspects that have not been explored in this model. For example, individuals in stepping stones produce offspring, which can help to keep up genetic variability. In our modelling approach, we only considered the effect of stepping stones on the target patch. We did not investigate whether the total productivity of the landscape regarding species’ numbers has increased and with that genetic variability, which is an important feature in conservation biology. In general, our results are reflections of the same effect: a trade-off caused by stepping stones. The positive effects are the production of additional dispersers. This effect is the more pronounced the larger the stepping stones are. These advantages are counteracted by two negative effects: an increase of the effective contagion also of the avoided habitat as well as an emerging shading effect (Bender and Fahrig 2005; Fahrig 2007).

It is also very important to bear in mind that the example modelled here is the specific conservation issue of the lynx with specific movement parameters that cannot easily be extrapolated to another species. This is because functional connectivity is a species specific concept which must be seen from the perspective of the individual (Baguette and Van Dyck 2007). Nevertheless, the proposed scenarios are realistic for the lynx in Europe and the same approach can be adopted for other rare species of conservation concern. Therefore, a future challenge is to address the general question under which species traits stepping stones are effective, depending i.e. on increasing daily dispersal distance, different behavioural responses or reproductive success, and landscape configurations. Considering demographic traits has already been proven crucial (Revilla and Wiegand 2008). It would also be interesting to investigate the time horizon when certain landscape configurations lead to colonisation success, i.e. search time sensu Tischendorf and Fahrig (2000a). We have shown with this example how the effect of stepping stones can be assessed for individual species. We found that there are many open questions regarding stepping stones, and that it cannot be answered in general whether they have a beneficial or negative effect. Especially when individual numbers are low due to demographic traits or small habitat patches, stepping stones may not compensate for the negative effects of habitat loss and fragmentation. We therefore suggest to carefully consider the existing situation before advocating stepping stones for conservation planning.