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Keywords:

  • boundary permeability;
  • cost of dispersal;
  • habitat fragmentation;
  • metapopulation;
  • Proclossiana eunomia

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix
  • 1
    We studied the consequences of behaviour at habitat patch boundaries on dispersal for the bog fritillary butterfly Proclossiana eunomia Esper in two networks of habitat differing in fragmentation and matrix quality. We tested for differences in responses to patch boundaries according to the fragmentation level of the network by analysing movement paths of adult butterflies.
  • 2
    Butterflies systematically engaged in U-turns when they reached a boundary in the fragmented network while they crossed over boundaries in more than 40% of boundary encounters in the continuous one.
  • 3
    We applied the Virtual Migration model (Hanski, Alho & Moilanen 2000) to capture–mark–recapture data collected in both networks. The model indicated (i) a lower dispersal rate and (ii) a lower survival during dispersal in the fragmented network. This latter difference is likely to be the key biological process leading to behavioural avoidance of patch boundary crossings.
  • 4
    On the basis of this behavioural difference, we designed an individual-based simulation model to explore the relationship between patch area, boundary permeability and emigration rate.
  • 5
    Predictions of the model fitted observed results of the effect of patch area on emigration rate according to fragmentation: butterflies are more likely to leave small patches than large ones in fragmented landscapes (where patch boundary permeability is low), while this relationship disappears in more continuous landscapes (where patch boundary permeability is high).

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

Dispersal, that is the movements of organisms between suitable habitat patches, is a key process in population biology, shaping the characteristic texture of populations, communities and ecosystems in space and time (Wiens 2001). Two complementary, but still rarely overlapping approaches consider dispersal as a major explanatory factor of population persistence within landscapes. In landscape ecology, ‘the degree to which the landscape facilitates or impedes movement among resource patches’ (i.e. landscape connectivity: Taylor et al. 1993) depends on how organisms perceive and move through the different portions of their habitat; this determines how individuals distribute in the landscape (e.g. Wiens, Stenseth & Ims 1993; Wiens 1997, 2001), which in turn influences population dynamics and generates distribution patterns. In metapopulation biology, the intensity of dispersal affects the relative importance of local processes (birth and death rates) vs. regional processes (immigration and emigration rates) to metapopulation dynamics (Hanski 1991, 1999; Thomas & Kunin 1999). Although with both the landscape ecology and the metapopulation approaches the starting point of dispersal through the matrix is individual behaviour at habitat patch boundaries (Haddad 1999; Jonsen & Taylor 2000; Matthysen 2002), this particular point has rarely been studied directly. The effect of landscape structure on behaviour at habitat patch boundaries is even more poorly known.

Butterflies are excellent model organisms for the study of dispersal, and a great deal of information has been gathered on dispersal patterns (i.e. between–patch exchanges) in butterfly metapopulations (e.g. Harrison, Murphy & Ehrlich 1988; Hanski & Kuussaari 1995; Petit et al. 2001; Wahlberg et al. 2002). Moreover, several empirical studies document how dispersing individuals behave in the matrix and locate suitable habitat patches (Conradt et al. 2000; Conradt, Roper & Thomas 2001). Theoretical models of metapopulation dynamics generally assume that the emigration rate is higher out of smaller habitat patches, because encounters with patch boundaries are more frequent, and indeed some empirical butterfly studies support this hypothesis (Hill, Thomas & Lewis 1996; Kuussaari, Nieminen & Hanski 1996; Thomas & Hanski 1997; Baguette, Petit & Queva 2000; Petit et al. 2001; Wahlberg et al. 2002). However, we have shown previously that the emigration rate was dependent on the fragmentation level of the landscape (Baguette et al. in press; Mennechez, Schtickzelle & Baguette in press). Indeed, in the bog fritillary butterfly Proclossiana eunomia Esper, the comparison of dispersal patterns between a highly fragmented and a more continuous landscape using capture–mark–recapture revealed a significant drop of dispersal in relation to fragmentation. Moreover, dispersal in both landscapes was affected by patch area effects on emigration rates in the highly fragmented landscape only. In light of previous observations of butterflies performing exploratory movements out of the departure patch, followed by returns at irregular intervals after a flight over unsuitable habitats (Baguette et al. 1998), we suggested that in fragmented landscapes butterflies are more reluctant to leave a patch − where they may find mates, oviposition sites and food supply − to fly through the ‘hostile’ matrix (Mennechez et al. in press). Habitat fragmentation is therefore associated with a cost of dispersal through the matrix, due to predation risk and the uncertainty of reaching another suitable habitat patch (e.g. Olivieri & Gouyon 1997; Andreassen & Ims 1998; Heino & Hanski 2001). Therefore, in opposition to a simple diffusion process, we hypothesize that dispersal out of a suitable habitat patch is an individual decision dependent on the perception of boundaries and resulting in habitat patch boundary crossings. Our decision hypothesis is supported by recent experimental evidence indicating that butterflies use visual cues to locate landscape elements (Dover & Fry 2001). Compared to fragmented landscapes, the cost of dispersal should be much lower in more continuous landscapes due to the very close proximity of suitable habitat patches. Therefore, we hypothesize that in more continuous landscapes, where butterflies cross patch boundaries more freely, dispersal will correspond much more to a diffusion process. The effect of patch area on emigration rates in the highly fragmented landscape was interpreted in the light of the cost of dispersal hypothesis (Mennechez et al. in press). In large patches, individuals will be reluctant to leave because of resource abundance, while in smaller patches resources may be limited, triggering dispersal of butterflies in spite of its cost. Consequently, the number of resident butterflies will be very low in such small patches.

In this paper, we investigate whether or not behavioural processes determine emigration out of a suitable habitat patch (the starting point of dispersal within the matrix). To do this we (i) tracked individuals and investigated whether movement paths differed between two isolated patch networks of contrasting fragmentation levels, and (ii) investigated differences in dispersal rates between the two networks using capture–mark–recapture methods. In the highly fragmented network, we expect that (i) spatial patterns of movement paths, reflecting behavioural decisions, differ at patch boundaries, and (ii) emigration rates should be lower. In the more continuous network we expect that (i) no differences exist between the spatial patterns of paths close or far from the patch boundary, and (ii) emigration rates should be higher. It is worth noting that the habitat fragmentation process is associated with extensive modifications in the matrix quality: in the highly fragmented network, both suitable habitat and the original, natural matrix are destroyed and replaced by large tracts of forests or intensively managed agricultural fields or pastures; on the contrary, habitat patches and the matrix are nearly undisturbed in the continuous network.

Then we turn to the cost of dispersal hypothesis: applying the Virtual Migration (VM) model (Hanski et al. 2000) to capture–mark–recapture data, we search for differences in mortality during dispersal between the two networks. Under this hypothesis we expect significantly higher dispersal mortality in the highly fragmented network. Finally, we develop a simulation model to explore how behaviour at habitat patch boundary affects emigration rates and their relationship with patch area. By modifying boundary permeability, i.e. the probability that a potential emigrant crosses the patch boundary (e.g. Stamps, Buechner & Krishnan 1987), we investigate how contrasting relationships between emigration rate and patch area may occur.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

the species

In Western Europe, the bog fritillary butterfly is a specialist species living in unfertilized wet meadows or in peat bogs, where the only food plant of larvae and adults, the bistort Polygonum bistorta L., grows. Modern cultural practices have transformed suitable habitats into improved pastures or spruce Picea abies (L.) Karst plantations. Other sites have been abandoned and overgrown. As a consequence, remaining populations of the butterfly are highly fragmented. Previous studies have shown that (i) the mating system of the bog fritillary is polygynous (Baguette & Nève 1994), (ii) male mate-locating behaviour is patrolling (Baguette, Convié & Nève 1996) and (iii) adults fly in one generation between the end of May and the beginning of July (Schtickzelle, Le Boulengé & Baguette 2002).

study system

The bog fritillary forms metapopulations in the Plateau des Tailles upland in southern Belgium (Nève et al. 1996; Nève, Mousson & Baguette 1996). In this landscape, we selected two networks of patches with contrasting fragmentation levels (Fig. 1, Table 1). The highly fragmented network (denoted by FRAG) is the Prés de la Lienne nature reserve (50°18′ N, 5°49′ E) where the bog fritillary forms a patchy population of 9 patches (totalling c. 2·3 ha of suitable habitats) in a highly fragmented landscape (Petit et al. 2001; Schtickzelle et al. 2002). The more aggregated network (denoted by AGGREG) is situated in the Pisserotte nature reserve (7 patches totalling c. 1·9 ha of suitable habitats; 50°13′ N, 5°47′ E). The main difference between the two sites lies in the fragmentation level (higher in FRAG) and the naturalness of the matrix: highly artificial in FRAG (mainly spruce plantations or fertilized pastures) vs. natural in AGGREG (undisturbed peat bog).

image

Figure 1. Map of the two study systems: Prés de la Lienne is highly fragmented (FRAG) and Pisserotte is more aggregated (AGGREG). Habitat patches are shown in grey; the limit of each system has been defined by the minimum convex polygon around all patches.

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Table 1.  Description of the fragmented (FRAG) and the aggregated (AGGREG) networks. Rather than drawing arbitrary borders to the networks, we used the method of minimum convex polygon to surround suitable habitat patches (see Fig. 1)
 Fragmented network (FRAG)Aggregated network (AGGREG)
Network
 TypeFarmlandNatural peat bog
 Size (ha)c. 17·8c. 6·1
 Suitable habitat (%)13%31%
Patches
 Number of patches97
 Mean patch size (ha)0·26 ± 0·170·27 ± 0·17
 Mean distance to other suitable384 ± 288125 ± 104
 patches (m) [range][0–943][0–364]

individual tracks

Females of P. eunomia were tracked individually to record movement path, during the 1994 flight season in FRAG and the 2002 flight season in AGGREG. Only females were tracked because (i) female dispersal is biologically much more important for metapopulation persistence, as it allows recolonization or the rescue effect (Fownes & Roland 2002; Hanski et al. 2002), and (ii) males are restless and fly too fast to allow effective recording. Each female was followed until it was lost from view or stopped for 15 min, and every stop of the female in its path was marked by a numbered flag. Using stops instead of sampling at fixed time intervals is biologically more meaningful, each stop corresponding to a decision made by the individual, and prevents problems of over- or undersampling due to the choice of the time interval between samplings (Turchin 1991, 1998). At the end of each recording, the coordinates of each flag were determined in order to obtain a map of the path with all its moves, allowing computation of quantitative variables. For practical reasons (i.e. paths were done during different years in both networks), different methods were used to determine coordinates, without any consequence in terms of results: relative to a fixed point using a theodolite in FRAG, determined by triangulation from measured distances to reference points located by a GPS in AGGREG. Based on different checks in the field, we know that the imprecision of FRAG data is a few cm, while in AGGREG it is lower than 50 cm, which is below the path resolution (only a few moves in AGGREG imply a length shorter than 1 m).

analysis of path data

The flight between two consecutive stops is not totally linear but in many cases, including that of butterflies, it can be appropriately summarized by a sequence of straight line moves and associated turning angles (Fig. 2; Root & Kareiva 1984; Turchin, Odendaal & Rausher 1991; Turchin 1998). Such representation of movement paths is the base of random walk models widely used in simulation models of animal movement (e.g. Turchin 1991, 1998). Move length and turning angles were computed from the stop coordinates and extensively analysed by statistical methods appropriate for movement path data (Turchin 1998 and references therein) and circular data (Fisher 1993 and references therein; see also Mardia 1972 and Zar 1999 chapters 26–27). All data management and analyses were done using the SAS System (SAS Institute Inc. 1999), some tests (for circular data) being programmed into SAS code because they were not available as standard in the SAS system. We chose to present test results in tables to make the text more readable and to offer an easy overview of all the hypotheses tested on the data as well as references to the tests used, several of them being uncommon and highly specific.

image

Figure 2. Schematic representation of a path showing the two main quantities which it can be summarized into: Li = length of the ith move; θi = turning angle between moves i and i + 1.

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dispersal within networks

Capture–mark–recapture data are available for 11 generations (1992–2002) for the FRAG metapopulation (Schtickzelle et al. 2002; Schtickzelle 2003) and one generation (2002) for the AGGREG metapopulation. We used the Virtual Migration (VM) model (Hanski et al. 2000; see also Appendix) to estimate several dispersal parameters at the metapopulation level, including emigration rate and mortality during dispersal; only data concerning females were used because path data were collected for females only. Although the number of patches is slightly too small to allow optimal parameter estimation with the VM model (n  10 is recommended), results can be compared between the two networks as uncertainty is reflected in the confidence limits of parameter estimates. It has already been successfully applied on part of the FRAG data set (1992–97: Petit et al. 2001) and such a comparison of VM parameter estimates, but between different species, has also been made by Wahlberg et al. (2002). We are aware that FRAG could be considered as two subnetworks (the two ends) which are not really far more fragmented than AGGREG. Nevertheless, due to the small number of patches it is not possible to run the VM model on subsystems, which would not be meaningful anyway because the whole FRAG network constitutes a single patchy population where the two subsystems are connected by frequent individual movements (Petit et al. 2001). Therefore, it is highly likely that the results observed in FRAG are representative of the whole FRAG network and are not largely dominated by processes occurring inside the two subnetworks, which would have caused a methodological problem when comparing the fragmentation level of FRAG and AGGREG. Estimated parameters were used to simulate (with the VM simulation module) dispersal in each system according to population size (estimated with Constrained Linear Models as in Schtickzelle et al. 2002), which notably gives an estimate of butterfly days spent in and outside the natal patch.

emigration rate predicted by simulation of movement paths

In order to explore the relation between emigration rate, habitat patch area and patch boundary permeability, we set up a simple individual-based simulation model. Ten simulations of 1000 paths each were made for each combination of the following parameter values: habitat patch area (0·1–4·6 ha by 0·3 ha; round patches were used to keep the model simple), boundary permeability (0–1 by 0·05), and maximum number of moves per path (20–140 by 20). Starting from the patch centre, a movement path is simulated by sampling successive move lengths and turning angles from estimated distributions (on pooled sites). When a move crossed the patch boundary, a value was sampled from a uniform distribution; if this value was smaller than the specified boundary permeability, the individual was counted as emigrating and the simulation continued with a new path; otherwise, the individual was considered to react to the boundary by making a U-turn and the move was directed towards the patch centre and the path continued normally thereafter. The boundary permeability is therefore defined as the probability of crossing the patch boundary upon reaching it. If the individual was still in the patch when the maximum number of moves was reached, it was counted as a non-emigrant and a new path was started. When the 1000 paths of the parameter combination were computed, the emigration rate was calculated as the fraction of paths leading to emigration. At the end of the 10 simulations, the mean of the 10 emigration rates (one per simulation) was calculated for each parameter combination.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

Seventeen paths totalling 223 stop points (5–20 per move) were mapped in FRAG while 36 paths totalling 524 stop points (4–60 per move) were mapped in AGGREG. These differences only reflect the different sampling efforts in both systems. These paths can be summarized by two main quantities (Fig. 2): the move length (distance between two consecutive stops) and the turning angle (angle between the directions of two consecutive moves).

move length

The distribution of move length has been characterized for each network and for pooled data (Table 2). Move length follows a log-normal distribution in both networks (Table 3 tests 1a and 1b) which does not significantly differ between the two networks (Table 2; Table 3 tests 2a and 2b) but differs significantly between paths in a given network (Table 3 test 2c). This means that females of P. eunomia tend to fly relatively short distances between successive stops but sometimes are able to make far longer movements, and that some paths present longer moves than others but without any relation to the network in which the path occurred. No autocorrelation (order 1–5) between the consecutive move lengths of a given path was detected in both networks (Table 3 tests 3a and 3b): females do not tend to move short or long distances into specific sequences, i.e. the length of a given move does not depend at all on the length of the previous moves.

Table 2.  Parameters of the move length (in m) distribution (log-normal) for each network, separately and pooled
NetworknMeanSDMinimum5th percentileMedian95th percentileMaximum
FRAG2068·309·040·30·75·027·547·0
AGGREG4886·837·630·30·74·224·049·4
Pooled6947·278·090·30·74·525·149·4
Table 3.  Statistical tests on move length; tests 1–2c are concerned with the move length distribution, tests 3a and 3b with autocorrelation in consecutive move lengths
 Null hypothesis testedTest nameTest statisticP-valuesReference
Test 1aLog-normal distribution: FRAGKolmogorov-SmirnovD = 0·050> 0·15Sokal & Rohlf (1995)
Test 1bLog-normal distribution: AGGREG D = 0·018> 0·15(pp. 708–715)
Test 2aEquality of variance between networksBartlett (on log-transformed move length)inline image= 3·060·08Sokal & Rohlf (1995) (pp. 396–401)
Test 2bEquality of means between networksHierarchical 2-way anova (on log-F1;51 = 0·120·73Sokal & Rohlf (1995)
Test 2cEquality of means between paths of a given networktransformed move length)F51;641 = 1·96< 0·0001 (pp. 272–320)
Test 3aNo autocorrelation between length of consecutive moves: FRAGPearson's correlation coefficient on consecutive lengths1 significant (P < 0·05) rho out of 55Sokal & Rohlf (1995) (pp. 559–560)
Test 3bNo autocorrelation between length of consecutive moves: AGGREG(with lag = 1–5)6 significant (P < 0·05) rhos out of 115 

turning angle

The distribution of turning angles is by definition circular, which makes the use of special statistical techniques necessary; the parameters of this distribution (mean m and concentration parameter K) were estimated for each network separately and for pooled data (Table 4). It is, in both networks, unimodal and centred on 0 (Table 5 tests 1a and 1b) and symmetrical around 0 (Table 5 tests 2a and 2b): females do not show a preference for left or right turns but turn as frequently in one direction as in the other and with the same amplitude. For each network, it is not significantly different from a von Mises distribution (Table 5 tests 3a and 3b; see also Fig. 3), which is a reasonable distribution under conditions of a correlated random walk: the von Mises distribution is the circular equivalent of the Normal distribution for linear quantities (e.g. Fisher 1993, pp. 48–56). Neither the concentration parameter K (Table 5 test 4) nor the mean (Table 5 test 5) differ significantly between the two networks, which was already obvious from seeing the separate estimates (Table 4); the resultant mean does not significantly differ from 0 (Table 5 test 6). Consequently, a single von Mises distribution with mean = 0 and K ≈ 0·4 (illustrated on Fig. 3) could be used to specify turning angles in both networks. Globally, females fly in one network exactly as they do in the other. No autocorrelation (order 1–5) between the consecutive turning angles of a given path is detected in either sites (Table 5 tests 7a and 7b): a given turning angle (direction and amplitude) is not influenced by the previous ones. There is no correlation between the move length and the associated turning angle (Pearson's rho: FRAG: rho = −0·02, P = 0·75, n = 189; AGGREG: rho = 0·07, P = 0·12, n = 452): females do not show a tendency to turn more or less (in amplitude) when they move over a short distance than when they move over a long distance.

Table 4.  Parameters (in brackets: 95% confidence interval) of the turning angle distribution (von Mises) for each network separately and pooled; m: mean turning angle (in degrees); K: concentration parameter (0 = uniform distribution)
NetworknmK
FRAG189−11·43 (−41·86; 19·00)0·3979
AGGREG452−5·80 (−25·13; 13·52)0·3938
Pooled641−7·47 (−23·57; 8·63)0·3946
Table 5.  Statistical tests on turning angle; tests 1a to 6 are concerned with the turning angle distribution, tests 7a and 7b with autocorrelation in consecutive turning angles
 Null hypothesis testedTest nameTest statisticP-valueReference1
  • 1

    Original and complementary references can be found there; see also Mardia (1972).

  • 2

    Fisher (1993) (p. 84) presents a mistake.

Test 1aUniform vs. unimodal distribution with mean = 0: FRAGModified Rayleigh test for uniformity against a unimodalR = 0·195< 0·0001Fisher (1993) (p. 69)
Test 1bUniform vs. unimodal distribution with mean = 0: AGGREGalternative with mean = 0R = 0·196< 0·0001 
Test 2aSymmetrical distribution around 0: FRAGWilcoxon signed-rank testW+ = −0·2160·83Fisher (1993) (pp. 80–81)
Test 2bSymmetrical distribution around 0: AGGREG W+ = 1·4400·15 
Test 3aGoodness-of-fit for von Mises distribution: FRAGWatson's U2U2 = 0·0450·20Lockhart & Stephens 19852
Test 3bGoodness-of-fit for von Mises distribution: AGGREG U2 = 0·0550·10 
Test 4Equality of von Mises concentration parameter K between networksFisher fr; P-value estimated by permutation testfr = 0·1270·73Fisher (1993) (pp. 131–132)
Test 5Equality of von Mises mean m between networksWatson-Williams Tr; P-value estimated by permutation testTr = 0·1580·74Fisher (1993) (pp. 124–128)
Test 6von Mises mean = 0 (pooled networks)Unnamed specific testEn = −0·9190·36Fisher (1993) (pp. 93–94)
Test 7aNo autocorrelation between consecutive turning angles: FRAGCircular-circular (T-linear) correlation coefficient on4 significant (P < 0·05) rhos out of 55Fisher (1993) (pp. 151–153)
Test 7bNo autocorrelation between consecutive turning angles: AGGREGconsecutive turning angles (with lag = 1–5); P-value estimated by permutation test6 significant (P < 0·05) rhos out of 115 
image

Figure 3. Distribution of turning angles, showing a peak around 180° due to return tendency when reaching the patch boundary, clearly present in FRAG but not in AGGREG. Black line: observed density (kernel density estimate, i.e. a kind of moving average: Fisher 1993, p. 24ff); grey line: expected von Mises (i.e. circular normal) distribution.

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behaviour at the habitat patch boundary

In the FRAG network, females show an obvious trend to come back into the patch after having reached/crossed the patch boundary. In the AGGREG network, this trend also exists but occurs far less often; consequently, several females went in the matrix or travelled in more than one AGGREG patch during the path recording, an event never observed in FRAG. From a biological point of view, this means that patch boundaries are less permeable to butterfly movement in FRAG than in AGGREG, i.e. they represent stronger barriers to dispersal.

Three different types of results support this hypothesis. (i) The frequency of boundary hits involving a U-turn towards the patch is higher (Fisher's exact test P= 0·015) in FRAG: 11 out of 11 (100%) vs. 15 out of 26 (57·7%). (ii) In FRAG there is an obvious peak of U-turns (frequency of turning angles around 180° is higher than expected) which is absent in AGGREG (Fig. 3). and (iii) the overall area explored by butterflies is smaller in FRAG, as shown by the results concerning a statistic called net squared displacement (square of the distance between position after n moves and starting point inline image; Kareiva & Shigesada 1983; Turchin 1998). If the path is a straight line, inline image increases following a parabola, which represents the upper limit of possible inline image; if the path is an uncorrelated random walk, E(inline image) increases linearly; a inline image curving up indicates a persistence in the direction of movement (correlated random walk), while a inline image curving down indicates some barrier to dispersal (Turchin 1998). If we put together all inline image for each site (Fig. 4), we clearly see that in FRAG inline image curves down after reaching a certain value, corresponding to movements a bit shorter than the maximum length (83 m) of the patch where paths were observed, while in AGGREG such curving does not appear and some paths show a high inline image. Additionally, it is also interesting to look at inline image for each path and test for significant departures from correlated random walk. To do this test, we computed by bootstrap (Manly 1997) the 95% confidence limits of inline image: for each observed path, 1000 paths were simulated keeping the observed move lengths fixed (instead of sampling them because of their high variability between paths) but sampling the turning angles from the estimated von Mises distribution (Table 4); the test is therefore only about the turning angle distribution. The 95% confidence limits for inline image were estimated by the 25th and 975th percentiles of the simulated inline image for each move in each path. Two conclusions emerge from the results on individual inline image: (i) more paths show inline image being significantly too small (indicating the presence of some barrier to dispersal; example shown in Fig. 5) in FRAG than in AGGREG (35% (6/17) vs. 22% (8/36)); (ii) fewer paths show inline image being significantly too high (indicating a more orientated movement; example shown in Fig. 5) in FRAG than in AGGREG (0% (0/17) vs. 14% (5/36)). These differences are nevertheless not significant (Fisher's exact test P > 0·05), partly due to the small numbers of paths.

image

Figure 4. Examples of evolution of net squared displacement after n moves (square of the distance between position after n moves and starting point: inline image) according to the total distance travelled in these n moves (from the starting point). Top graph: one path (map in insert) in FRAG showing the return tendency when reaching the patch boundary (hence a low inline image). Bottom graph: one path (map in insert) in AGGREG showing the trend to longer and straighter movements (hence a high inline image), notably in the matrix. Filled symbols: observed inline image; open symbols: 95% confidence limits under correlated random walk.

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image

Figure 5. Evolution of net squared displacement after n moves (square of the distance between position after n moves and starting point: inline image) of all paths according to the total distance travelled in these n moves (from the starting point). In FRAG inline image, reaches a maximum corresponding to the maximal length of the patch, indicating that patch boundaries act as barriers to dispersal; in AGGREG, there is no limit to the increase of inline image, as the butterfly moves away for its starting point.

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dispersal within networks

Out of the 11 generations within the FRAG network, we kept those (1992, 1994, 1996 and 1997) which show at least 40 female interpatch movements; these four data sets total to 769 marked females, 1428 (re)captures and 269 interpatch movements. Capture histories were put end to end to allow the estimation of one set of mean parameters for these four generations with the VM model. The 2002 generation for the AGGREG network comprises 438 marked females, 1049 (re)captures and 296 interpatch movements. By pooling four FRAG generations to constitute a data set of comparable size to the AGGREG one, any random effects due to limited amounts of movement observed in each FRAG generation are reduced. The results are comparable as overall capture conditions (weather conditions and catch effort) were similar during all the years in both networks. The VM model estimates for these two networks are given in Table 6. As both networks contain a small number of patches, the successful partition of mortality between mortality during dispersal vs. mortality in the patch is not completely ensured. We therefore also ran the VM model with survival in the patch fixed to 0·95 and 0·90, plausible values for the bog fritillary in these networks (Schtickzelle et al. 2002). Confidence intervals on parameter estimates, and therefore statistical significance, is changed but no difference is inversed: parameters higher in FRAG always remain higher and vice versa.

Table 6.  Dispersal parameters (in brackets: 95% confidence limits) at the metapopulation level as estimated by the Virtual Migration model (Hanski et al. 2000): (a) without constraint, (b) survival in patch fixed at 0·95, (c) survival in patch fixed at 0·90. ϕp: survival in patch; η: emigration rate for a 1-ha patch; ζem: parameter scaling the dependence of emigration rate on patch area; α: parameter scaling the effect of distance on isolation; λ: parameter scaling mortality during dispersal; ζim: parameter scaling the dependence of immigration rate on patch area. See Appendix for equations involving these parameters
ParameterFRAGAGGREGDifference between networks: significant (*) or not (NS)
(a)
 ϕp1·0000 (0·9211; 1·0000)0·9235 (0·9058; 0·9494)NS
 η0·2187 (0·1483; 0·2596)0·2904 (0·2295; 0·3521)NS
 ζem0·2787 (0·1529; 0·4451)0·0662 (0·0000; 0·2178)NS
 α4·6449 (4·0352; 5·3142)9·7677 (7·4392; 12·2818)*
 λ0·7137 (0·3900; 1·0236)0·0708 (0·0000; 0·3984)*
 ζim0·6039 (0·3741; 0·8603)0·0000 (0·0000; 0·1015)*
(b)
 ϕpFixed at 0·95Fixed at 0·95n.a.
 η0.1807 (0·1482; 0·2195)0·2990 (0·2347; 0·3670)*
 ζem0·3337 (0.1934; 0·4742)0·0792 (0·0000; 0·2309)NS
 α4·7524 (4·1002; 5·4373)9·2518 (6·8491; 11·8605)*
 λ0·5482 (0·3657; 0·8187)0·3352 (0·1504; 0·5865)NS
 ζim0·5999 (0·3419; 0·8606)0·0000 (0·0000; 0·1195)*
(c)
 ϕpFixed at 0·90Fixed at 0·90n.a.
 η0·1407 (0·1107; 0.1772)0·2904 (0·2294; 0·3502)*
 ζem0·4102 (0·2498; 0·5705)0·0642 (0·0000; 0·2156)*
 α4·8176 (4·1225; 5·5483)9·7770 (7·4370; 12·2801)*
 λ0·3513 (0·2247; 0·5435)0·0000 (0·0000; 0.1811)*
 ζim0·5832 (0·3171; 0·8517)0·0000 (0·0000; 0·1017)*

For the same patch connectivity, the mortality during dispersal (function of λ, see Appendix) is higher in the FRAG network. The emigration rate (function of η and ζem, see Appendix) largely changes according to patch area in FRAG but not in AGGREG. Several other indications exist at the network level of lower emigration in FRAG than in AGGREG, while the mean patch area is equivalent in both systems (Table 1): (i) more females stay their entire life in the same patch in FRAG (57·3% (47/82) vs. 42·1% (127/302); Fisher's exact test P= 0·017); (ii) less butterfly days are spent outside of the natal patch in FRAG (51·9% (3868/7448) vs. 71·7% (4452/6208); Fisher's exact test P < 0·0001); (iii) the number of successful dispersal events per female is lower in FRAG (1·18 (1388 for 1173 females) vs. 2·86 (1900 for 665 females)); (iv) none of the females followed in FRAG went out of the patch while several did in AGGREG; and (v) during capture–mark–recapture operations far fewer females were observed flying in the FRAG matrix than in the AGGREG matrix. In summary, females disperse less often in FRAG than in AGGREG, and when they do so they experience a higher mortality.

emigration rate predicted by simulation of movement paths

As expected, the emigration rate decreases both with increasing patch area and with decreasing boundary permeability (Fig. 6). The maximum number of moves per path influences the absolute value of emigration rate but not its relative value compared to other combinations of patch area and boundary permeability. Therefore, figures present data for the maximum number of moves = 60. The boundary permeability has two main effects on emigration rate: (i) the emigration rate increases with increasing boundary permeability, and (ii) it rapidly drops with increasing patch area when boundary permeability is low but is nearly constant when this permeability is high. These two effects can be illustrated by looking at the value of parameters from a power function of the patch area (as in the VM model, see Appendix) fitted to the emigration rate (Fig. 7): (i) the absolute value of the parameter scaling dependence to patch area (ζem) decreases (i.e. tends to 0) when boundary permeability increases, and (ii) the value of emigration rate for a 1-ha patch (η) increases with increasing boundary permeability. Notice also that as boundary permeability increases, the shape of the relationship between patch area and emigration rate shifts from a power function to a linear relation.

image

Figure 6. Decrease of emigration rate with increasing patch area and with decreasing habitat patch boundary permeability, as predicted by simulation model of correlated random walk. The effect of patch area is pronounced when boundary permeability is low (as in FRAG) but negligible when it is high (as in AGGREG). Shown for the maximum number of moves per path = 60.

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image

Figure 7. Effect of boundary permeability on the value of parameters determining the decrease of emigration rate with patch area (A) according to the following power function: inline image. Increasing boundary permeability leads to increased emigration rate for a given patch area (η) and decreased effect of patch area on emigration rate (ζem). Shown for the maximum number of moves per path = 60.

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

We compared here two networks of habitat patches differing in fragmentation level and matrix quality, but situated within the same landscape. This location was chosen to guarantee that environmental and historical factors affecting both P. eunomia metapopulations are comparable. Genetic tests using RAPDs indicate that the metapopulations are isolated from each other (Vandewoestijne & Baguette, unpublished data).

Although the paths were recorded during different years in the two networks, the observed differences can really be attributed to the effect of landscape structure and not to a temporal effect. Indeed, (i) all the paths were recorded under similar, favourable climatic conditions as it is well known that sunny and warm weather increases butterfly activity (e.g. Shreeve 1992); (ii) no behavioural differences were observed during the 11 years of capture–mark–recapture data collection in FRAG; and (ii) some paths were also recorded in the AGGREG network in the same year as in the FRAG network (1994) and they show the same characteristics as the AGGREG 2002 data set and the same differences from the FRAG 1994 data set. However these were not numerous enough to allow proper statistical comparison with the FRAG data set, which is the reason for the recording of new paths in AGGREG in 2002.

Our results clearly show that butterfly behaviour at patch boundaries was modified by habitat fragmentation. Analyses of track recordings using various complementary tests unanimously indicated that in the highly fragmented network (FRAG) butterflies approaching patch boundaries engaged in U-turns significantly more often than in the more aggregated one (AGGREG). Therefore, boundary perception by flying butterflies is evident here, as already reported by Schultz & Crone (2001) for another butterfly species. Additionally, we show here that boundary perception has different consequences depending on the fragmentation of the networks: while boundary crossing avoidance was the rule in the highly fragmented network, boundary crossings occurred quite frequently in the more aggregated network. This difference in behaviour corresponds to the biological process determining contrasting levels of boundary permeability (e.g. Stamps et al. 1987), because these behavioural differences directly affect the number of patch-boundary crossings leading to emigration. Except for the behaviour at patch boundaries, no difference between networks is seen in movement patterns (move length and turning angle distributions) – even when separately estimated, values are very similar, thus allowing us to exclude the possibility of too small sample sizes preventing us from detecting significant differences. All subsequent analyses of dispersal using capture–mark–recapture data at the network level revealed emigration rates lower in the highly fragmented network, which is in agreement with a limitation of dispersal with habitat fragmentation.

This general pattern of decreasing dispersal with increasing fragmentation level corresponds to the general predictions of theoretical models of the evolution of dispersal (Olivieri & Gouyon 1997; Heino & Hanski 2001). We go further here, by testing for the cost of dispersal hypothesis, which is the key parameter of such models (e.g. Wahlberg et al. 2002). Using the Virtual Migration model, we detected a significantly higher mortality during dispersal in the highly fragmented network than in the more aggregated one. This result is not surprising as it corresponds to selection pressures that shape the evolution of behavioural responses to habitat patch boundaries, which are themselves the processes leading to the decrease in dispersal rates within fragmented landscapes. To our knowledge, this is the first time that such a cost of dispersal associated with fragmentation has been empirically demonstrated.

This difference in dispersal mortality has to be related to the fact that, for dispersing butterflies, the matrix matters (Ricketts 2001). As we pointed out earlier, there was a striking difference in the quality of the matrix between the two networks, in term of naturalness: the matrix of the more aggregated AGGREG network (peat bog) was much more natural than in the other network (areas of afforestation or artificial pastures). The landing of dispersing butterflies in the more natural matrix of the AGGREG network was recorded several times during individual tracks, while this was never the case in the matrix of the highly fragmented FRAG network. Therefore, we propose that, besides the classical risks associated with dispersal in the matrix (predation or uncertainty of reaching suitable habitats), whether or not the matrix offers the possibility for interruption of interpatch travel may be an important factor for dispersal survival.

The relationship between emigration rate and patch area was found to be different according to the fragmentation level of the landscape: the widely accepted pattern of decreasing emigration with increasing patch area, generally observed in fragmented landscapes (e.g. Hill et al. 1996; Kuussaari et al. 1996; Thomas & Hanski 1997; Kindvall 1999; Baguette et al. 2000; Petit et al. 2001; Wahlberg et al. 2002) with consequences for metapopulation persistence (Kindvall & Petersson 2000), was challenged by the comparison of bog fritillary butterfly dispersal between a continuous and a highly fragmented landscape (Mennechez et al. in press). In this latter study, no relationship was detected between patch area and emigration rate in the continuous landscape, while emigration rate out of small patches was significantly higher than out of larger patches in the highly fragmented landscape. Our simulation model of butterfly movements in patches with different permeability provides predictions in good qualitative agreement with these empirical results. The decreasing effect of patch area on emigration rate when the habitat patch boundary permeability increases can be explained as follows. When the permeability is low, potential emigrants have to reach the patch boundary several times before crossing over it, because they return frequently into the patch. The number of boundary hits rapidly decreases as the patch becomes larger, leading to a lower emigration rate. However when the permeability is high, only a few hits are needed to trigger boundary crossing and so lead to emigration. Thus, with high permeability, even in a large patch potential emigrants encounter the boundary at a high enough frequency to allow emigration, leading to a reduced effect of patch area. These predictions correspond to empirical data obtained in the present study: we showed that boundary permeability in the FRAG network can be considered as low (butterflies engaged in U-turns when they reached a patch boundary), and indeed we report a high effect of patch area on emigration rate. On the other hand, in the AGGREG network patch permeability may be considered higher (butterflies cross over patch boundaries in more than 40% of patch boundary encounters), and the effect of patch area on emigration rate is limited.

Our results indicate that a metapopulation model assuming that emigration rate decreases with increasing patch area is not always realistic, and is justified only when boundary permeability is low. Specifically, the use of such a function parameterized with data from one landscape to predict emigration rate in another landscape is not appropriate, unless the boundary permeability can be assumed to be roughly the same, that is if the quality of the matrices is similar. Our results offer a clear warning against using unconsidered generalizations in population viability analysis and conservation biology.

In conclusion, our study provides a coherent picture of the effect of fragmentation on dispersal. We suggest that the lower survival of dispersing individuals in the fragmented habitat patch network that we document here is the key biological process at the basis of the evolution of behavioural avoidance of patch boundaries. According to this hypothesis, this behaviour will in turn induce the difference in dispersal rate patterns observed in the comparison between fragmented and continuous patch networks. It is worth noting that habitat fragmentation occurred over a maximum of 30 butterfly generations in the FRAG network (Baguette et al., in press). An example of such an evolution of dispersal ability related to habitat fragmentation has been shown to occur in Plebejus argus L. (Thomas, Hill & Lewis 1998). An alternative hypothesis is that butterflies respond to subtle differences in the properties of habitat patch boundaries between the two networks, because matrix quality was very different in the two environments. According to this hypothesis, Kuussaari et al. (1996) showed that the quality of patch boundary influences movement rates in the butterfly Melitaea cinxia L. Experimental releases in the same patches of butterflies collected from the two networks, and subsequent comparative analyses of their movement paths, will help to rigorously solve this critical issue.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

Julie Choutt, Isabelle Convié, Iwona Mróz, Gabriel Nève and Beata Paciejewska took part in data collection. Atte Moilanen provided help with the VM model. A first draft of this manuscript was greatly improved by insightful comments from Ilkka Hanski, Otso Ovaskainen and Chris D. Thomas, as well as from two anonymous referees. This work was funded by the Belgian National Fund for Scientific Research through a ‘research fellow’ (mandat d’aspirant FNRS) grant to N.S. and by a grant from the Office of Scientific, Technical and Cultural Affairs (Belgian Federal Government) to M.B. (contract OSTC-PADD II EV10/16 A, 2000–04). Special capture licenses for P. eunomia and site access were provided by the ‘Ministère de la Région Wallonne’. This is contribution BRC016 of the Biodiversity Research Centre.

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  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix
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Appendix

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendix

We present here a brief summary of the Virtual Migration (VM) model (Hanski et al. 2000) and its equations to facilitate interpretation of results. The VM model estimates the parameters of survival and dispersal for individuals in a metapopulation based on capture histories from a multi-site capture–mark–recapture study. Connectivity of the patches is assumed to influence mortality during dispersal but not mortality within a habitat patch, allowing the separate estimation of these two mortalities.

The parameters to be estimated are:

  • Survival in habitat patch: ϕp

  • Emigration rate from patch j according to its area Aj:

    • image
  • Connectivity of patch j according to distance djk between j and each other patch k and area Ak of patch k:

  • image

Survival during dispersal as a sigmoidally increasing function of connectivity Sj: inline image