Measuring functional connectivity using long-term monitoring data


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1. We use population synchrony as a new empirical method to assess functional connectivity – the permeability of landscapes given species dispersal attributes. Functional connectivity is important because well-connected metapopulations are expected to be more resistant to stochastic events causing extinction.

2. A variety of factors impact population synchrony, and we attempt to account for several of these (shared climate, distance, habitat similarity and location within the range) before investigating impacts of the suitability of the landscape between populations – a proxy for permeability to dispersal.

3. For the Speckled Wood butterfly (Pararge aegeria), we find that population synchrony is positively correlated with landscape suitability, suggesting that synchrony might be used to measure functional connectivity.

4. The importance of landscape suitability for population synchrony shows a humped relationship with distance – suitability has no effect between 0 and 20 km, then showing a significant positive effect above 20 km but with reduced (still significant) effect from 160 to 200 km. This suggests that relatively close populations may exchange sufficient migrants for synchronisation, regardless of the matrix suitability. In contrast, more separate populations are synchronised only where the landscape permits functional connectivity, most likely through dispersal between intermediate stepping-stone populations.

5.Synthesis and applications. We show that patterns of synchrony in long-term monitoring data can be used to estimate functional connectivity of landscapes. As such, this technique might be used to test and prioritise the effectiveness of land management for conservation of species and to mitigate the effects of climate change.


The biological impacts of climate change are well documented (Parmesan et al. 1999; Root et al. 2003; Hickling et al. 2006), and a focus of current conservation policy is to facilitate the movement of species across landscapes to mitigate the effects of environmental change (Hodgson et al. 2009). In this context, functional connectivity is the permeability of a landscape to the dispersal of individuals (With, Cadaret & Davis 1999; Goodwin & Fahrig 2002). Dispersal across landscapes is essential for range expansion (colonisation of new sites), maintenance of genetic diversity and metapopulation persistence (rescue of locally extinct sites) (Gilpin & Hanski 1991; Hanski 1998). Although dispersal rates typically exhibit a distance-decay pattern, Ricketts (2001) showed that the intervening matrix between sites significantly determines ‘effective isolation’, i.e. isolation is not based purely on geographic distance between sites but also on the type, quality and configuration of the intervening matrix.

The ‘matrix’ between sites is often defined as the region of non-habitat (Dover & Settele 2009), but defining what is habitat for a species is not always straightforward (Dennis, Shreeve & Van Dyck 2003), and areas of matrix may also contain resources that species use (e.g. nectaring resources for butterflies; Dover & Settele 2009). Therefore, in our study, we define ‘matrix’ simply as the inter-site landscape. The permeability of the matrix is defined as the degree to which the matrix promotes the movement of individuals between sites and for butterflies, may be facilitated by a) features that aid directed movement or b) features that provide habitat resources such as nectaring plants or even host plants to form intermediate ‘stepping-stone’ populations (Dover & Settele 2009). Highly permeable, less hostile matrix between sites leads to populations that are ‘functionally connected’.

Given the crucial importance of functional connectivity for conservation, especially in human-modified, fragmented landscapes undergoing rapid climate change, we urgently need ways to measure it to test the suitability of landscapes appropriately. Mark–release–recapture (MRR) techniques allow the movement rates of individuals to be assessed, but these techniques are very time-consuming, expensive and can miss rare, long-distance dispersal events (Elzinga et al. 2001). Also, the individual movements assessed in MRR studies may be qualitatively different from long-distance dispersal events, which these studies fail to capture (Van Dyck & Baguette 2005). An emerging set of alternative techniques, landscape genetics, involve an assessment of the genetic similarity of populations, under the assumption that well-connected populations will have lower genetic diversity between populations (Manel et al. 2003; Storfer et al. 2007). Although promising, these techniques are still currently expensive and time-consuming. A further complicating factor is the time since the population was founded; the genetic differentiation between populations is a function of not just spatial separation but also temporal separation.

In this paper, we investigate the possibility of using a new technique to assess functional connectivity empirically using long-term annual population time-series data from discrete spatial locations. In northern Europe particularly, such data are available from a number of existing monitoring schemes. We believe that this technique has the potential to offer an invaluable conservation tool to measure functional connectivity and to prioritise conservation land management. We use long-term population time-series data to measure population synchrony, the correlations in time series of abundance indices between sites. Evidence suggests that shared climate, natural enemies and also the dispersal of individuals between sites can all affect synchrony between populations (Moran 1953; Hanski & Woiwod 1993; Sutcliffe, Thomas, & Moss 1996; Lande, Engen, & Saether 1999; Paradis et al. 1999; Bjørnstad & Bascompte 2001; Cattadori, Haydon, & Hudson 2005; Kerlin et al. 2007; Roland & Matter 2007; Matter & Roland 2010). Roland & Matter (2007) show that for an alpine butterfly species (Parnassius smintheus) synchrony is determined by distance through forest, with intervening forest decreasing dispersal between alpine meadow sites. In addition, sites with similar habitats or management regimes may also show increased synchrony (Sutcliffe, Thomas, & Moss 1996; Paradis et al. 2000). Species may also show spatial variation in synchrony across their geographic ranges (Powney et al. 2010). Using a technique known as ‘prewhitening’, it is possible to account for the synchrony caused by large-scale shared climate (Paradis et al. 2000) and therefore investigate factors impacting residual synchrony. This residual synchrony can then be related to characteristics of the landscape matrix, with other factors that affect synchrony added into the statistical model as control variables. We hypothesise that residual synchrony will be higher between sites that are separated by a less hostile matrix, as measured by a bioclimatic model. Sites that are separated by more suitable landscape are more likely to have linked population dynamics. We believe that an increase in functional connectivity will increase dispersal between sites and, in turn, increase synchrony through a combination of rescue effects, site colonisation and source-sink mechanisms (Pulliam 1988; Gilpin & Hanski 1991; Hanski 1998). We also predict that the importance of matrix quality will be greatest for long-distance dispersers, as individuals can fly directly between nearby sites without needing to use matrix resources.

Materials and methods

Data collation

Population time series for the Speckled Wood butterfly (Pararge aegeria) were taken from the United Kingdom Butterfly Monitoring Scheme (UKBMS). This butterfly species was chosen as it is a widespread, abundant species, and information regarding its ecology and behaviour is well known (Asher et al. 2001; Fox et al. 2006). Pararge aegeria is a woodland species with larvae that feed on a number of different grasses. The adults are found in a range of different habitat types such as hedgerows and grassland, especially in warmer regions (Asher et al. 2001). The rapid range expansion of the species into new areas in recent years suggests considerable dispersal capability (Asher et al. 2001), although the rate of expansion is limited by availability of habitat at the expansion range margin (Hill, Thomas, & Huntley 1999). The UKBMS survey is carried out by observers walking line transects during 26 weeks between April and September recording all butterflies within set criteria for weather and time of day conditions. From these data, an index of abundance for each species at each site each year and a national collated index of abundance were calculated (ter Braak et al. 1994; Rothery & Roy 2001). The national collated index was converted from a log scale to a normal scale by taking the exponential and then standardising to unity. Further details of the UKBMS survey technique can be found in the study by Pollard & Yates (1993) and in Roy et al. (2001). A distribution map of sites used in our analysis can be found in Appendix S1.

The habitat type of each monitoring site was categorised into one of six classes (agricultural land, woodland, grassland, heathland, wetland and other). The habitat type ‘other’ was composed mainly of transects described as bare ground, ornamental parks, church lawns or missing a description. Habitat data for the matrices between sites were taken from a remotely sensed land cover map (CEH Land Cover Map 2000 – LCM2000; Fuller et al. 2002) with 13 aggregated habitat categories (Appendix S2).

Population synchrony between sites

Annual counts and the collated indices of P. aegeria from 1976 to 2008 in each transect were extracted from the UKBMS database. We used prewhitening and detrending to remove global synchronising factors enabling us to examine the residual population time series (Paradis et al. 2000). Some sites in the data set showed long-term trends in abundance. To account for this, prior to prewhitening, annual abundance indices from each site were detrended by taking the residuals from a linear model of abundance index with year. Visual inspection of raw data confirmed that a linear model adequately removed any long-term trends. We then prewhitened these data, adding a range of scaling factors to the equation in the study by Paradis et al. (2000) to optimise the sensitivity of the prewhitened data to matrix suitability. The equation is as follows:


where dit is the prewhitened count for the ith site in year t, cit is the detrended raw abundance index for the ith site in year t, s is the scaling factor, μi is the mean abundance of site i and It is the value of the national collated index for year t. Scaling factors tested were 0·05, 0·1, 0·25, 0·5, 1, 1·5 and 2. We also carried out the analyses on raw index values (s = 0). These scaling factors were chosen as they give a broad coverage along a scale moving from raw count data with global synchronicity still present (scaling factor of zero) to data that more closely resemble the global time series (scaling factor of 2). Pearson cross-correlation coefficients were then calculated on the prewhitened data to identify residual synchrony between all pairs of transects. A chain of zero abundance counts followed by positive values (associated with new site colonisation) can inflate synchrony values and in turn increase Type I errors (Sutcliffe, Thomas, & Moss 1996). We therefore excluded transects that had more than 25% of the yearly abundance counts of < 3 (Sutcliffe, Thomas, & Moss 1996). To ensure data quality, pairs of transects with < 7 years of common data records were omitted from the analysis (Sutcliffe, Thomas, & Moss 1996).

Matrix hostility between sites

Using a presence-only species distribution model, MAXENT (Phillips, Anderson, & Schapire 2006), we estimated landscape suitability for P. aegeria in each 1-km cell in Great Britain. Presence data for the butterfly at 1-km spatial scale were obtained from the Butterflies for the New Millennium Survey between 1995 and 2004 (Asher et al. 2001; Fox et al. 2006). The species distribution data in the Millennium Atlas were collected at a range of scales from 10 m to 10 km. The data are available at the 1-km grid cell scale but, to improve display quality, are presented in the atlas distribution maps at the 10-km scale (Asher et al. 2001). The butterfly data were collected by a large number of recorders (> 200) based across Britain (Asher et al. 2001). These recorders submitted the records to local coordinators who then fed the data back to a central database (Asher et al. 2001). To ensure data quality, records were only accepted if they met a minimum data standard (essential information of each record: species name, grid reference, location, date, recorders name, number seen). Effort was made to improve the geographic coverage of the data through targeted surveying (Asher et al. 2001). More detailed information on the methods used to obtain butterfly distribution data can be found in chapter 3 of ‘The Millennium Atlas of Butterflies in Britain and Ireland’ (Asher et al. 2001). Environmental layers used in the species distribution model were the proportions of each of the 13 aggregated Landcover map habitat categories in each 1-km cell. We did not include climate data in our model, because our aim was to use the model to assess the suitability of the matrix to dispersing butterflies. Our a priori expectation was that habitat cover, but not average climate, would affect landscape permeability. This expectation later proved correct as the MAXENT estimate of landscape suitability estimated without climate data was a better fit to population synchrony than with climate data; therefore, we only present results for the former.

For all combinations of pairwise site comparisons, we calculated the average MAXENT value of habitat suitability for all 1-km cells in a 3-km-wide rectangular buffer between sites, which we consider to be representative of the zone through which most dispersing butterflies will move. We also repeated the analyses using a 5-km buffer, a 7-km buffer and additionally calculated habitat suitability between sites using a least cost pathway metric with one minus habitat suitability as the cost. However, the 3-km buffer was the landscape scale that produced the best fit to population synchrony between sites, and therefore, we present only these results.

Statistical analysis

First, we fitted a linear regression to data from all transect pairs with synchrony as the response variable. The mean landscape suitability estimated by MAXENT in the 3-km buffer between sites was our explanatory variable of interest. However, to account for variation in synchrony caused by habitat similarity, distance between sites and position in range, we also included these three measures as additional explanatory variables. Distance was calculated as the Euclidean distance between sites (km), habitat similarity as a binary variable (1 = same broad habitat type, 0 = different habitat type) from the broad habitat classifications given to each UKBMS site and position in range as the ‘northerliness’ (km northing) of the most northerly site of a pair. We used pairwise site comparisons up to 200 km apart (n = 37190, Appendix S4). Because of the non-independence of pairwise comparisons, the significance of each explanatory variable was estimated by 1000 Mantel randomisations (Manly 1998; Kerlin et al. 2007). To check for colinearity between the explanatory variables, variance inflation factors for the model were identified using the vif function, using the CAR package in the program R (Fox & Weisberg 2010). As a rule of thumb, variance inflation factors > 10 are considered to indicate colinearity.

Second, to assess how the importance of matrix suitability changed with increasing distance between sites, we split the pairwise site comparisons into 20-km-distance bands (0–20 km, 20–40 km, etc). Using the same aforementioned linear model structure, we fitted ten separate models, one to each of the distance band subsets (between 0 and 200 km) of the total data set. Once again, Mantel randomisations were used to identify the significance of matrix suitability on synchrony. All statistical analysis was carried out using R 2·7·2 (R Development Core Team 2008).


The MAXENT model showed that the distribution of P. aegeria was negatively associated with heathland and positively associated with deciduous woodland, consistent with previous knowledge of the species’ habitat requirements (Asher et al. 2001). The model produced a reasonable fit to the species distribution data (model area under curve (AUC) = 0·783), and the full MAXENT habitat association table for P. aegeria is given in Appendix S3.

As described in the methods section, we added various scaling factors into our prewhitening step. We repeated the full model relating population synchrony to site and landscape characteristics using prewhitened data with different scaling factors to identify the scaling factor that optimised the sensitivity of the analysis to landscape suitability. The sensitivity of the analysis was measured as the matrix suitability t-value taken from the full model. The optimum scaling factor for detecting a relationship between population synchrony and matrix suitability was 0·05 (Table 1). Results presented from hereon are based on data that have been prewhitened with a scaling factor of 0·05.

Table 1.   Coefficients of matrix suitability taken from the full model of synchrony based on data which have been prewhitened using eight different scaling factors. A scaling factor of 0·05 (in bold) optimises the sensitivity of the data to landscape suitability
Scaling factorRegression coefficientStandard errort valueMantel P
08·61 × 10−17·94 × 10−210·848<0·001
0·051·0768·19 × 10−213·142<0·001
0·11·0858·26 × 10−213·137<0·001
0·251·0728·47 × 10−212·66<0·001
0·58·96 × 10−18·64 × 10−210·373<0·001
12·49 × 10−17·86 × 10−23·167<0·001
1·5−4·14 × 10−26·19 × 10−2−0·6690·236
2−8·75 × 10−24·59 × 10−2−1·9060·034

All four explanatory variables (landscape suitability, habitat similarity, position in range and distance between sites) were significant (using Mantel randomisation tests) in explaining synchrony (Table 2). Synchrony was positively correlated with landscape suitability and negatively correlated with distance (Fig. 1). Reduced hostility of the matrix between sites was therefore associated with increased synchrony between populations. Synchrony was positively correlated with both habitat similarity and position in range (km northing; Table 2). All explanatory variables in the model had VIF values < 10; therefore, there was little evidence of colinearity.

Table 2.   Coefficients from the minimum adequate model explaining synchrony between populations of Pararge aegeria. Mantel randomisation tests were used to determine significance of each variable
Explanatory variableRegression coefficientStandard errort valueMantel P
Matrix suitability1·0928·03 × 10−213·596<0·001
Distance (km)−6·66 × 10−44·32 × 10−5−15·435<0·001
Habitat similarity2·70 × 10−24·20 × 10−36·423<0·001
Northing (km)3·82 × 10−43·77 × 10−510·131<0·001
Figure 1.

 (a) The relationship of residual synchrony with increasing suitability of the intervening landscape for comparisons between sites 0–200 km apart. Residual synchrony is plotted after removing the effect of relationships between distance, habitat similarity and position in range (km northing) with population synchrony. Each point represents the mean residual synchrony value of all pairwise comparisons between transects for each 0·01 interval of matrix suitability. Points with < 50 sites comparisons with high standard error, and therefore inaccurate mean estimates, were removed from the figure. (b) The relationship between residual synchrony and geographic distance for site comparisons between 0 and 200 km apart. Residual synchrony is plotted after removing the effect of habitat similarity, matrix suitability and position in range (km northing) on synchrony. Each point represents the mean residual synchrony value of all pairwise comparisons between transects for each 10-km-distance intervals.

Synchrony was significantly positively correlated with suitability of the intervening matrix between sites for sites between 20 and 200 km apart (Fig. 2). For sites approximately 60–160 km apart, the composition of the intervening matrix had the greatest effect on population synchrony (Fig. 2) However, for sites < 20 km apart, the suitability of the landscape was less important for maintaining functional connectivity between populations. Hence, the importance of landscape suitability for synchrony exhibits a humped relationship with distance (Fig. 2), with the importance of matrix suitability beginning to decline after 160 km.

Figure 2.

 The relationship between the importance of matrix suitability in explaining population synchrony and distance between sites. The importance of matrix suitability is the regression coefficient for the relationship between matrix suitability and synchrony for each 20-km-distance band. Asterisks above each bar indicate whether regression coefficients are significantly different from zero determined by Mantel randomisation tests (***P < 0·001, **P < 0·01, *P < 0·05).


In this study, we find a negative correlation between distance and local population synchrony at relatively large spatial scales. This confirms the results of previous studies which suggest that the negative correlation is because of reduced successful dispersal and increased differences in environmental conditions between sites that are further apart (Moran 1953; Hanski & Woiwod 1993; Sutcliffe, Thomas, & Moss 1996; Lande, Engen, & Saether 1999; Paradis et al. 1999). Our results also confirm that population synchrony is higher between sites of similar habitat types and sites that are closer to the species’ range margin (Sutcliffe, Thomas, & Moss 1996; Powney et al. 2010). However, our main result is the positive correlation between the suitability of the intervening matrix and population synchrony, independent of the aforementioned factors. This suggests that, after accounting for other factors that promote synchrony, the remaining residual population synchrony may be suitable for measuring the movement of individuals between populations, i.e. functional connectivity across landscapes.

The importance of landscape suitability in explaining synchrony shows a humped relationship with distance. At short distances (< 20 km), populations are highly synchronised (Fig. 1b) but the quality of the intervening matrix is less important at explaining synchrony than at greater distances. We suggest that this may be because P. aegeria can disperse directly between sites (over hostile matrices) at short distances, which reduces the importance and dependence on landscape suitability. Pararge aegeria is a mobile species that is often found outside of, but close to, woodland. Hence, such short-distance movements between woodland patches over unsuitable landscapes (e.g. agricultural fields) are frequently observed (Merckx & Van Dyck 2005, 2007). These results support the contention that functional connectivity need not always require physical connectivity of habitats (With, Cadaret, & Davis 1999). Ricketts (2001) suggested that rather than connecting sites using habitat corridors, instead, we may be able to alter the permeability of the matrix between sites through management practices. Many current agri-environment schemes aim to make the wider landscape around protected areas less hostile to species. The technique we present here could potentially be used to measure the permeability of such landscape matrices.

At larger spatial scales (> 20 km), the importance of landscape permeability in determining synchrony is significant. This result shows that even at large spatial scales, matrix quality is important in maintaining functionally connected populations. We suggest that this effect of matrix suitability on butterfly population synchrony is not a consequence of individual butterflies dispersing across extremely large distances (up to 200 km), but rather a case of multiple, connected stepping-stone populations. Dover & Settele (2009) suggested stepping stones may be adequate for functional connectivity. The MAXENT model predicts the probability of occupancy of each grid cell by butterflies. Therefore, sites separated by cells with a higher probability of occupancy are more likely to have linked stepping-stone populations, which will result in linked dynamics. After accounting for other known synchronising factors, our results suggest that populations of P. aegeria may be functionally connected at large distances, although the importance of matrix suitability began to decline after 160 km, and we predict that the importance of landscape suitability would eventually become non-significant as distance between sites increases above 200 km. Other authors have also shown theoretically and empirically that dispersal can cause synchrony over large spatial scales and our results support this contention (Haydon & Steen 1997; Stenseth et al. 1998; Bjørnstad, Ims, & Lambin 1999; Lundberg et al. 2000; Ranta, Lundberg, & Kaitala 2006).

As funding for conservation is limited, there is great pressure to spend efficiently. One method to increase efficiency is to prioritise conservation efforts spatially (Moilanen, Wilson, & Possingham 2009). The ability to measure functional connectivity using long-term monitoring data would be particularly useful to these spatial conservation prioritisation efforts. As functional connectivity is the ability of the landscape to facilitate the dispersal of organisms, metapopulations in areas with low functional connectivity may suffer from increased extinction risk (Gilpin & Hanski 1991; Hanski 1998; With, Cadaret, & Davis 1999; Goodwin & Fahrig 2002). Regions where synchrony and functional connectivity are low could be considered priority zones for landscape manipulation. These areas will benefit from targeted land management to increase landscape permeability. In addition, increasing landscape permeability will facilitate the movement of species through landscapes as ranges shift under changing climates (Parmesan et al. 1999; Root et al. 2003; Hickling et al. 2006). At the other end of the spectrum, theoretical work shows that very high levels of synchrony in metapopulation dynamics may lead to increased extinction risk (Gilpin & Hanski 1991). This suggests that there may be an optimal level of functional connectivity for metapopulation persistence. However, most animal populations show low enough levels of synchrony, even between nearby populations, that the threat of global extinction is not generally regarded as high (Piha et al. 2007).

Although we have interpreted our findings in relation to dispersal, it is important to consider other possible causes of the correlation between matrix suitability and synchrony. First, and perhaps most importantly, natural enemy populations can impact population synchrony (Bjørnstad & Bascompte 2001; Cattadori, Haydon, & Hudson 2005; Kerlin et al. 2007; Vogwill, Fenton, & Brockhurst 2009). If movements of natural enemies are related to our measures of landscape suitability, then this may be reflected in the relationship between matrix suitability and butterfly population synchrony, i.e. we have assessed not only butterfly functional connectivity but also butterfly natural enemy functional connectivity. This hypothesis is hard to discount without further theoretical or empirical study into the distribution and dispersal of natural enemies of butterflies. However, a separate study shows that synchrony between populations of the ringlet butterfly (Aphantopus hyperantus) is strongly correlated with actual dispersal events from mark–recapture data (L. K. Broaders & T. H. Oliver, unpublished). Hence, synchrony does show promise as a valuable tool to measure functional connectivity of butterfly populations.

A second potential cause for the relationship between matrix suitability and population synchrony could be woodland management. Many small patches of woodland (associated landscapes with a high proportion of unsuitable matrix) may be managed more heterogeneously (many owners) than large continuous areas of woodland (suitable matrix). Heterogeneity of management in regions with low matrix suitability may cause reduced synchrony between sites. Contrary to this hypothesis, however, large tracts of woodland are often managed to be heterogeneous to promote biodiversity (Sutherland & Hill 1995; Benton, Vickery, & Wilson 2003). Therefore, woodland management is unlikely to explain the patterns we found.

In conclusion, we find a positive correlation between butterfly population synchrony and matrix suitability between monitoring sites, which is especially strong at relatively large spatial scales. This presents the intriguing possibility that synchrony could be used as a measure of functional connectivity between sites. At present, we cannot account for the impact that natural enemies can have on population synchrony and therefore cannot confirm that synchrony can be used to measure functional connectivity. We suggest further development of this technique to explore the relative impacts of natural enemies, climate and dispersal on population synchrony.


We are very grateful to all the recorders who contribute to the UKBMS. The UKBMS is a partnership between Butterfly Conservation and the Natural Environment Research Council, Centre for Ecology & Hydrology. The UKBMS is funded by a multi-agency consortium led by Defra and includes the Countryside Council for Wales, the Joint Nature Conservation Committee, Forestry Commission, Natural England, the Natural Environment Research Council, the Northern Ireland Environment Agency and Scottish Natural Heritage. We thank Colin Harrower for advice regarding statistical analysis. We also thank Chris Thomas and Kevin Watts for useful discussion.