693

Can patterns of spatial autocorrelation reveal population processes? An analysis with the fi re salamander

Gentile Francesco Ficetola , Raoul Manenti , Fiorenza De Bernardi and Emilio Padoa-Schioppa

G. F. Ficetola (francesco.fi cetola@unimib.it) and E. Padoa-Schioppa, Dipto di Science dell ’ Ambiente e del Territorio, Univ. degli Studi di Milano- Bicocca, Piazza della Scienza 1, IT-20128 Milano, Italy. – R. Manenti and F. De Bernardi, Dipto di Biologia, Univ. degli Studi di Milano, Via Celoria 26, IT-20123 Milano, Italy.

Spatial autocorrelation (SAC) is often observed in species distribution data, and can be caused by exogenous, autocor-related factors determining species distribution, or by endogenous population processes determining clustering such as dispersal. However, it remains debated whether SAC patterns can actually reveal endogenous processes. We reviewed stud-ies measuring dispersal of the salamander Salamandra salamandra , to formulate a priori hypotheses on the scale at which dispersal is expected to determine population distribution. We then tested the hypotheses by analysing SAC in distribution data, and evaluating whether controlling for the eff ect of environmental variables can reveal endogenous processes. We surveyed 565 streams to obtain species distribution data; we also recorded landscape and microhabitat features known to aff ect the species. We used multiple approaches to tease apart endogenous and exogenous SAC: the analysis of residuals of logistic regression models considering diff erent environmental variables; the analysis of eigenvectors extracted by several implementations of spatial eigenvector mapping. In capture – mark – recapture studies, 98% of individuals moved 500 m or less. Both species distribution and environmental features were strongly autocorrelated. Th e residuals of logistic regression relating species to environmental variables were autocorrelated at distances up to 500 m; analyses considering diff erent sets of environmental variables, or assuming non-linear species habitat relationships, yielded identical results. Th e results of spatial eigenvector mapping strongly depended on the matrix of distances used. Nevertheless, the eigenvectors of models with best fi t were autocorrelated at distances up to 200 – 500 m. Th e concordance between multiple approaches suggests that 500 m is the scale at which dispersal connects breeding localities, increasing probability of occurrence. If exogenous variables are correctly identifi ed, the analysis of SAC can provide important insights on endogenous population processes, such as the fl ow of individuals. SAC analysis can also provide important information for conservation, as the existence of metapopulations or population networks is essential for long term persistence of amphibians.

‘I invoke the fi rst law of geography: everything is related to everything else, but near things are more related than distant things ’

Tobler (1970)

Spatial autocorrelation (SAC) is an unavoidable feature of spatial ecological data. SAC arises when nearby localities have similar values for a given parameter. For many years, SAC has been considered mainly as a noise biasing ecologi-cal models (Legendre 1993, Dormann 2007b): SAC violates the assumptions of independence of many classical statistical models (e.g. regression, ANOVA … ), and both species dis-tribution data and ecological parameters are often spatially autocorrelated (Lichstein et al. 2002, Wagner and Fortin 2005). Several analyses focused on the potential biases that can arise when SAC is not considered in models (Dormann 2007b), or identifi ed approaches to tackle the confounding eff ects of SAC, and remove them from models (Lichstein et al. 2002, Griffi th and Peres-Neto 2006, Dormann et al.

2007, Kissling and Carl 2008, Beguer í a and Pueyo 2009, Bini et al. 2009, Peres-Neto and Legendre 2010).

SAC is often caused by processes inherent to ecological systems. Th erefore, analysing the patterns of SAC instead than simply removing it from the models can provide key information on ecological processes. Two major pathways are recognised as sources of SAC (Wagner and Fortin 2005). First, species are often related to environmental variables (e.g. topography, habitat, resources … ) which are in turn spatially autocorrelated. In this case, SAC observed in spe-cies distribution is viewed as a simple consequence of the dependence of species from these exogenous variables (thus also named exogenous autocorrelation or spatial dependence sensu Legendre 1993). Furthermore, species distribution can be spatially autocorrelated because of endogenous ecological processes such as dispersal, aggregation or competition (also named endogenous autocorrelation; Chapman et al. 2009, Beale et al. 2010). Dispersal can be a major source of endog-enous SAC: nearby locations linked by dispersal can have mutually dependent population dynamics, leading to SAC

Ecography 35: 693–703, 2012 doi: 10.1111/j.1600-0587.2011.06483.x

© 2011 Th e Authors. Ecography © 2011 Nordic Society OikosSubject Editor: Pedro Peres-Neto. Accepted 13 September 2011

694

in species distribution (Liebhold et al. 2004, Wagner and Fortin 2005, Siesa et al. 2011).

Discriminating between endogenous and exogenous SAC may therefore provide key information on the actual processes determining species distribution, and help to infer endogenous processes (Liebhold et al. 2004, Chapman et al. 2009). In the-ory, exogenous SAC can be removed by models relating species to environmental features, assuming that all relevant, auto-correlated environmental variables are included in the model (Lichstein et al. 2002, McAbendoth et al. 2005, Dormann et al. 2007). Under such situation, the analysis of variation not explained by exogenous variables (e.g. the model residu-als, or the variables incorporated into models to describe the SAC pattern), can be used to infer endogenous SAC, and to describe potential underlying causes. However, a reliable infer-ence of endogenous processes from the analysis of distribution data can be diffi cult (Dormann 2009): residual SAC might also arise because of model misspecifi cation (e.g. lack of relevant predictors, or representing non-linear relationships as linear), making it problematic the identifi cation of endogenous param-eters (van Teeff elen and Ovaskainen 2007, Dormann 2009). Analysing species for which independent data on ecological processes exist, and comparing the analysis of SAC with more direct measurements of population processes, would allow to evaluate whether attempts of extraction of endogenous vari-ables from distribution data can provide useful results.

When exogenous forces are controlled for, nearby localities may have similar occupancy because of dispersal (Liebhold et al. 2004, Goldwyn and Hastings 2008). Amphibian popu-lations are often described as part of networks of metapopu-lations or patchy populations, and dispersal is viewed as the major endogenous process determining spatial distribution of populations (Marsh and Trenham 2001, Smith and Green 2005). Th e extent of connection among sub-populations infl uences the dynamics of species distribution; the assess-ment of the spatial scale at which populations are linked can also have conservation applications, for example to identify at which spatial scale management should be performed (e.g. what is the distance among populations that enables the main-tenance of a consistent fl ow of individuals and long term pop-ulation survival?) (Ficetola and De Bernardi 2004, Hanski and Gaggiotti 2004, Angelone and Holderegger 2009). Th is infor-mation is usually obtained through the analysis of population clusters, or measuring gene fl ow (Vos and Stumpel 1996, Vos et al. 2001, Ficetola and De Bernardi 2004, Rowe and Beebee 2007, Angelone and Holderegger 2009). Th e analysis of endogenous SAC may contribute a further approach to the measurement of connection among populations.

In this study, we combined models describing species – habitat relationships with the analysis of spatial autocor-relation, to evaluate the role of exogenous (environmental) and endogenous factors in determining the distribution of the fi re salamander Salamandra salamandra in northern Italy. Th e fi re salamander is an excellent species to evaluate whether the analysis of SAC can actually reveal endogenous processes: species ecology is well known, habitat models can explain a very large proportion of variation of species dis-tribution (Manenti et al. 2009b, Ficetola et al. 2011a), and several fi eld studies measured processes (e.g. movements, dis-persal) that can be the source of endogenous SAC. We used the deductive approach proposed by McIntire and Fajardo

(2009) to show how endogenous processes can be identifi ed from the analysis of spatial autocorrelation. On the basis of knowledge of species biology, we assumed that dispersal is the major endogenous process determining spatial distribu-tion/clustering of populations (Marsh and Trenham 2001, Liebhold et al. 2004, Smith and Green 2005). First, we reviewed the literature on salamander movements, to obtain an a priori hypothesis on the particular scale at which dis-persal is expected to aff ect population distribution. We then used multiple approaches to analyse SAC of S. salamandra distribution to test this a priori hypothesies: if SAC analy-sis can correctly infer the scale of endogenous processes, the results of SAC analysis would be congruent with the a priori hypotheses obtained through direct measurement of dispersal (McIntire and Fajardo 2009, pp. 50 – 51). Finally, we tested two alternative hypotheses on the potential sources of SAC: 1) residual SAC is caused by incorrectly representing complex relationships with linear terms; 2) SAC is caused by the lack of relevant environmental variables. We expect that, if these two hypotheses were valid, the SAC pattern would change when modifying model specifi cation.

Methods

Review of the literature

We reviewed the available literature to obtain information on salamander dispersal and movements, and therefore to formulate a priori hypotheses on the scale at which endoge-nous processes (fl ow of individuals, dispersal) are expected to aff ect the distribution of populations. We considered stud-ies providing data on movements through capture – mark – recapture; for each study, we measured the proportion of individuals performing movements at the diff erent distance classes, the average and the maximum movements. If not reported directly by the authors, distances were obtained from the fi gures in the papers. In some cases, average or raw data were not available, and we obtained the modal class instead. Results of this kind of studies may be aff ected by the size of the study area (i.e. studies investigating large areas are more likely to detect long-distance dispersal). Th erefore, we also recorded the maximum distance covered by the study sites (following Smith and Green 2005). We considered in our review also studies on the closely related S. infraimmaculata , which is similar to S. salamandra and was considered a subspecies of S. salamandra until recently (Steinfartz et al. 2000). We considered only studies with maximum covered distance � 200 m.

Study species, area and sampling

Th e fi re salamander S. salamandra is widespread in Europe, and shows high plasticity for habitat use and for reproductive strategies (N ö llert and N ö llert 1992, Manenti et al. 2009a). Adults are strictly terrestrial and live in broadleaved forests; only females migrate to wetlands to give birth to the aquatic larvae; newborns are usually laid in small streams. Between 2003 and 2006, we surveyed 565 sites (usually fi rst- or second-order streams) and the surrounding landscapes in a hilly area nearby the lake Como in northern Italy (Fig. 1). Th e

695

study area is a complex mosaic of croplands, urban settle-ments and broadleaved forests; forests cover about 49% of the landscape. Th e sites covered the whole altitudinal range (200 – 1400 m) of the species in the study area (Di Cerbo and Razzetti 2004).

We used visual encounter surveys (Crump and Scott 1994) to evaluate the presence of larvae of fi re salaman-der in the 565 sites; per each stream, we surveyed sectors of 100 m. Each site was surveyed at least twice during the most suitable period for larval deposition and occurrence (end of February – beginning of May, September – beginning of November). Th e per visit detection probability in each site was � 0.9, therefore two visits allow an adequate assess-ment of species distribution (Mazzoleni 2005, Manenti et al. 2009b, Ficetola et al. 2011b). For each site, we recorded the hydroperiod as 1) non-ephemeral (it retained water during all the visits) or 2) ephemeral (it was dry during at least one visit). Larval development of the fi re salamander requires at least three months; therefore our measure of hydroperiod is relevant for survival probability. Furthermore, we recorded two landscape features on the basis of the vector map of Lombardy ( � www.cartografi a.regione.lombardia.it � ): for-est cover in a radius of 400 m, and density of hydrographic network in a radius of 600 m from the sites. Forest cover represents the availability of terrestrial habitat for the adults, while a dense hydrographic network increases the possibility of existence of population networks; previous studies showed that the distribution of the fi re salamander is strongly related

to these landscape variables measured at these spatial scales (Ficetola et al. 2009).

Statistical analyses

We used two methods to evaluate the scale of SAC, and to test our hypotheses about endogenous SAC. First, we evaluated the pattern of SAC of species distribution, of environmen-tal variables, and of the residuals of an ordinary least squares (OLS) logistic regression relating species distribution to the three environmental variables measured in all the 565 sites.

Second, we evaluated the pattern of SAC of eigenvec-tors extracted by spatial eigenvectors mapping (SEVM). SEVM is a technique translating the spatial arrangement of data points into a series of eigenvectors capturing the spatial eff ects (Dormann et al. 2007). Th e identifi cation of relevant eigenvectors has been proposed as an indication of scale at which spatial autocorrelation aff ects the data, and perhaps of the endogenous SAC (Diniz-Filho and Bini 2005, Dormann et al. 2007, see also Dormann 2009). SEVM is a unique approach to express spatial structure through eigenvectors, however the generation and selection of eigenvectors has been performed using diff erent criteria (also referred to as variants). In SEVM, eigenvectors can be generated through two approaches: principal coordinates of the neighbourning matrice (PCNM), which represents the spatial confi gura-tion of points through principal coordinates of a distance matrix among points (Borcard and Legendre 2002), and Moran eigenvector maps (MEM), which is an improvement of PCNM: in MEM, positive eigenvectors always represent signifi cant autocorrelation (Dray et al. 2006, Peres-Neto and Legendre 2010). In both PCNM and MEM, the num-ber of generated eigenvectors can be large; it is therefore important performing eigenvector selection, to reduce their number and improve the chance of identifying signifi cant environmental fractions.

In our analyses, we used three diff erent variants of SEVM. 1): ‘ 30 eigenvectors ’ variant. We generated eigenvectors using PCNM (Borcard and Legendre 2002), considering positive eigenvectors only; as spatial predictor, we added to the model the expected species presence, estimated by a linear combi-nation of the fi rst 30 eigenvectors alone (Diniz-Filho et al. 2008, p. 482). 2): ‘ Moran ’ s I reduction-PCNM ’ variant. We generated eigenvectors using PCNM as in 1), but we added eigenvector(s) to an OLS model, until the spatial autocor-relation of residuals, measured using global Moran ’ s I, was non-signifi cant (Griffi th and Peres-Neto 2006, Dormann et al. 2007). In this approach, we therefore selected the eigenvector(s) best reducing spatial autocorrelation (Griffi th and Peres-Neto 2006, Dormann et al. 2007); we tested the signifi cance of residual Moran ’ s I using a permutation test (Lichstein et al. 2002). Th is approach is similar to ‘ variant 3 ’ of SEVM used by Bini et al. (2009), and is considered among the most robust spatial methods (Dormann et al. 2007, Bini et al. 2009). 3): ‘ Moran ’ s I reduction-MEM ’ vari-ant. We generated vectors using MEM (Dray et al. 2006), and we selected them as described for variant 2) (Dormann et al. 2007).

SEVMs calculate eigenvectors on the basis of a matrix of distances among sites; we compared diff erent approaches

Figure 1. Study area and distribution of sites sampled (empty dots: Salamandra salamandra absent; fi lled dots: S. salamandra present; pale gray, forested areas; dark gray, major waterbodies). Due to geo-graphic proximity, some dots are superimposed.

696

frequently represented in models as linear terms; this form of model misspecifi cation may aff ect SAC patterns. To assess this hypotheses, we repeated the analysis of residuals using binomial generalized additive models (GAMs) instead than logistic regression. GAMs are a semi-parametric extension of generalized linear models, in which the response curves are data driven. GAMs are particularly suited for evaluat-ing curvilinear relationships in species-habitat relationships (Wood 2006, Ficetola and Deno ë l 2009), and allow to take into account potential non-linear relationships between sala-mander distribution and habitat. Comparing the residuals of models with and without non-linear terms allows to assess whether non-linearity is a determinant of the SAC pattern. We fi tted GAMs using the package MGCV in R (Wood 2006, R Development Core Team).

Analyses considering different environmental variables

To evaluate whether residual SAC is caused by lack of pre-dictors, we repeated the analysis of residuals over a subset of 132 streams. For these sites, four further variables describing stream features, communities and (indirectly) water quality were available: maximum depth; morphological heterogene-ity of the stream (measured on the basis of the percentage of alternation of seeps, riffl es and pools; Petersen 1992); richness of macrobenthos communities (measured using the extended biotic index, EBI) and abundance of periphyton (see Manenti et al. 2009b for details on the measurement of these variables). Th e variable hydroperiod was not con-sidered, as all these streams were non-ephemeral. Th e model including these additional variables explained a much larger proportion of variation than the one including three variables only (Results); comparing the residuals of models explaining a diff erent amount of variation can therefore help to evalu-ate whether adding further key predictors would change the pattern of SAC.

Results

Review of the literature: direct observations on dispersal

We found six studies reporting measures of movements or dispersal in S. salamandra (4 studies) or S. infraimmacu-lata (2 studies), representing 326 individuals. All studies reviewed showed a limited extent of terrestrial movements of salamanders (Table 1). In fi ve studies, the maximum disper-sal distance was � 503 m, and � 90% of individuals moved � 200 m, in some cases over several years. Only one study, performed on S. infraimmaculata , detected movements at distances � 1000 m (4% of individuals) (Bar-David et al. 2007); the maximum distance was 1280 m. If data from the six studies are pooled together, 96% of individuals moved � 200 m, 2% of individuals moved 200 – 500 m, while only 2% moved distances � 500 m.

Th e maximum distance measured was positively related to the longest possible measure in the study site (Spearman ’ s correlation, r S � 0.94, n � 6, p � 0.005). Nevertheless, even

proposed for building distance matrices, to evaluate the eff ect of this somehow subjective decision on the interpreta-tion of results. We calculated eigenvectors on the basis of A) distances obtained using a Gabriel network, following Bini et al. (2009); B) geographic distances; considering seven pos-sible truncation distances, which allows to give more weight to short-distance eff ects (Diniz-Filho and Bini 2005): 200, 500, 750, 1000, 1500, 2000 and 3000 m. Five-hundred meters represent the scale at which residual SAC of the OLS model is observed (see Results; approach suggested by Diniz-Filho and Bini 2005); distances up to 1500 m represent the maximum dispersal distances reported by diff erent studies on dispersal of Salamandra salamandra and related species (see Review of the literature: direct observations on dispersal; Glandt 1986), and therefore represent possible approaches integrating a priori information on population processes in the analyses. Distances up to 3000 m represent possible larger scale dispersal, since fi eld studies might underestimate the actual extent of amphibian movements; furthermore, 3024 m represents the distance that keeps all sites linked (Borcard and Legendre 2002). Using 3024 m instead than 3000 m yielded identical results (not shown).

We did not use approaches based on autologistic regres-sion (van Teeff elen and Ovaskainen 2007) because we sam-pled only a subset of potential localities of presence, and because analyses of simulated data suggest that the results can be unreliable and diffi cult to interpret (Dormann 2007a, 2009, Dormann et al. 2007, Betts et al. 2009). For each analysis, we used Moran ’ s I to build correlograms measuring SAC at multiple distance classes: 200, 500, 750, 1000, 1500, 2000, 3000, 4000, 5000, 10 000, 20 000 and 30 000 m. In the analyses of SEVMs, we standardized I by dividing by its maximum (I STD � I/max I), because I of eigenvectors did not vary strictly between – 1 and � 1 (Lichstein et al. 2002).

If necessary, variables were transformed to improve nor-mality using squareroot (length of hydrographic network) or arcsine-squareroot (forest cover). We used Akaike ’ s informa-tion criterion (AIC) to compare models. AIC is a measure of relative performance of models combining amount of explained variation and number of parameters included in the model; models explaining more variation with less vari-ables have lower AIC values and are considered to be ‘ best ’ models (Burnham and Anderson 2002). Using AIC cor-rected for small sample size would provide identical results (not shown). We also calculated Nagelkerke ’ s R 2 (R 2 N ) as a measure of the amount of variation explained by regression models; we used variance partitioning to assess the amount of variation explained by environmental and spatial vari-ables (i.e. the spatial eigenvectors). In all models and for all variables, variance infl ation factor was � 2, indicating that collinearity did not strongly aff ect our models. We per-formed statistical analyses using the package SPDEP under the R environment (Bivand 2010, R Development Core Team); we built correlograms using SAM 3.1 (Rangel et al. 2010).

Analyses considering non-linearity of relationships

Model misspecifi cation is a further potential cause of residual SAC. Ecological relationships are often non-linear, but are

697

had very similar AIC values (Table 2c). Within the ‘ Moran ’ s I reduction-MEM ’ models, the model with a truncation distance of 200 m was the one explaining more variation and with the lowest AIC. All the ‘ Moran ’ s I reduction ’ models included only one eigenvector, as it was enough to reduce residual SAC to nonsignifi cant values.

Th e pattern of SAC of eigenvectors was remarkably dif-ferent among the implementations (Fig. 3). For models using the matrix of geographic distances, SAC of eigen-vectors was generally strong, positive and signifi cant at distances � than the truncation distance (Fig. 3a – g). For models using Gabriel network, SAC of eigenvectors was positive and signifi cant at distances up to 5000 m for the two PCNM variants, while SAC was weaker and with large associated standard errors for the ‘ Moran ’ s I reduction-MEM ’ variant (Fig. 3h). In most of cases, when considering the same truncation distances, the autocor-relation of eigenvectors was similar in the three variants (Fig. 3).

Th e results of variance partitioning were diff erent between the three variants (Table 2). For Moran ’ s eigenvec-tor models, in all cases most of variation was explained by the independent eff ect of environmental variables (Table 2c – d). For the 30 eigenvectors variants, environmental variables still explained the largest amount of variation, but a consistent amount of variation was accounted for by the joint eff ect of environmental and spatial (i.e. the spatial eigenvectors) variables. Th e independent eff ect of spatial eigenvectors accounted for 15 – 20% of explained variation (Table 2b). In all variants, the joint eff ect of environmental and spatial variables increased at the large truncation distances ( � 1000 m) (Table 2).

Was autocorrelation caused by non-linearity of relationships?

Th e generalized additive model explained more deviance than the model including linear terms only ( R 2 N � 0.39), and suggested that the relationship between salamander distribution and forest cover may be non-linear and rather complex (Supplementary material Appendix 1, Fig. A2; χ 2 � 99.4, DF � 8.7, p � 0.0001). Th e relationship between salamanders and hydrographic network was weaker and lin-ear ( χ 2 � 1.3, DF � 1, p � 0.255); also in this model, sala-manders were strongly associated to non ephemeral streams

in the two studies investigating the largest spatial extent, about 95% of individuals moved 500 m or less. On the basis of these observations, we hypothesized that the most of fl ow of individuals occurs at distances up to 500 m.

Field study: spatial autocorrelation of variables

We detected larvae of S. salamandra in 242 out of 565 sites (43%; Fig. 1). Th e distribution of S. salamandra was strongly autocorrelated. SAC was strong at distances up to 500 m (I � 0.23); nevertheless, SAC remained positive and signifi cant at distances up to 5000 m (Fig. 2a). Spatial autocorrelation refl ected strong clustering of species dis-tribution: most occupied sites were near to other occu-pied localities (Fig. 1). Furthermore, most environmental variables were aff ected by strong SAC (Supplementary material Appendix 1, Fig. A1).

Ordinary least squares model

Th e OLS model relating salamander distribution to the three environmental variables explained 36% of variation according to Nagelkerke’s R 2 (Table 2a); as observed by pre-vious analyses considering much smaller datasets (Ficetola et al. 2009, Manenti et al. 2009b), salamanders were sig-nifi cantly associated to permanent streams surrounded by high forest cover, while the relationship with hydrographic network was non signfi ciant (Table 2a; Supplementary material Appendix 1, Table A1). Th e residuals of the OLS model were spatially autocorrelated at scales up to 500 m (Fig. 2b).

Spatial eigenvector mapping

In most of cases, SEVMs had better fi t and lower AIC than OLS (Table 2). Th e ‘ 30 eigenvectors ’ variant tended to explain more variation, and had lower AIC values, than the two ‘ Moran ’ s I reduction ’ variants (Table 2b – d). Th e ‘ 30 eigenvectors ’ models with truncation distances of 200 – 500 m had the lowest AIC and explained the largest propor-tion of variation ( ∼ 45%; Table 2b). Within the ‘ Moran ’ s I reduction-PCNM ’ models, the model with a truncation dis-tance of 1500 m was the one explaining more variation and with the lowest AIC. However, nearly all the other models

Table 1. Movements of Salamandra salamandra and S. infraimmaculata reported in the literature. n: number of individuals considered by each study.

Distance classes (m)

Max. (m) Mean (m) Modal classLongest measure of study site (m)Reference n � 200 200 – 500 500 – 750 750 – 1000 1000 – 1500

Deno ë l 1996 68 99% 1% 222 22 400Joly 1968 (Berc é Forest) 97 100% a 48 a (250) b 12 300Joly 1968 (La Fl è che) 8 100% 136 67 220Schulte et al. 2007 c 37 92% 5% 3% 503 88 610Bar-David et al. 2007d 72 89% 4% 1% 1% 4% 1280 0 – 200 m 8850Degani and Warburg 1978 d 44 100% 160 0 – 10 m 280

a territorial individuals only; b breeding migrations; c considering movements of � 30 d only; d study performed on S. infraimmaculata (formerly S. salamandra infraimmaculata ).

698

Figure 2. Pattern of spatial autocorrelation of (a) distribution of Salamandra salamandra in 565 sites; (b): residuals of OLS linear regression models relating the distribution of Salamandra salamandra to three environmental variables (565 sites analysed); (c): residuals of GAM, assuming non-linear relationship between salamander distribution and wood cover (565 sites analysed); (d) residuals of a model considering six environmental variables (123 sites analysed). Error bars are twice the standard error of Moran ’ s I; asterisks indi-cate spatial autocorrelation signifi cantly � 0.

( χ 2 � 39.8, DF � 1, p � 0.0001). Nevertheless, the pattern of residual autocorrelation remained unchanged. SAC of residuals was high and signifi cant at distances up to 500, while it tended to zero at larger distances (Fig. 2c).

Was autocorrelation caused by missing variables?

Th e model including the four additional environmental variables, run over the 132 streams dataset, was highly sig-nifi cant ( χ 2 6 � 111.8, p � 0.0001; Supplementary material Appendix 1, Table A1) and explained a large proportion of variation (R 2 N � 0.764). Th is model explained much more variation than the one including just three variables, and considerably more than all the SEVMs (compare with Table 2); further details on the relationships between S. sal-amandra and these additional environmental variables are reported elsewhere (Manenti et al. 2009a, b). Nevertheless, the pattern of residual autocorrelation remained unchanged. SAC of residuals was high and signifi cant at distances up to 500, while it tended to zero at larger distances (Fig. 2d).

Discussion

Spatial autocorrelation is increasingly considered a key feature in the analysis of ecological data. However, so far SAC has been mostly considered a trouble to remove from models; only a few studies explored autocorrelation as a resource for the understanding of ecological processes (Legendre 1993, Ficetola 2008, Chapman et al. 2009, Conlisk et al. 2009). Our combination of information on species movement, and analysis of SAC in species distri-bution models suggests that it is possible to tease apart endogenous and exogenous processes that can determine SAC, and correctly identify the scale at which endogenous processes occurs.

Th e review of available literature on salamander shows that distance poses important limitations to movements: in all reviewed studies, 90% or more of individuals moved � 200 m, while dispersion events � 500 m were extremely rare ( � 2% of individuals; Table 1). A possible limitation of our review is that most of studies focused on adults, while juveniles might move longer distances (Joly 1968). Nevertheless, the single study considering also sub-adults (Deno ë l 1996) did not obtain diff erent fi ndings. Th erefore, even if the available measures of species movements might be conservative (Bar-David et al. 2007), they probably corre-spond well to the actual dispersal of the majority of individuals. Th ese available information thus indicate that most individuals disperse over distances of 500 m or less (Glandt 1986).

SAC was pervasive in our data sets: nearly all the envi-ronmental features measured (landscape, microhabitat and biotic communities) were autocorrelated (Supplementary material Appendix 1, Fig. A1). For landscape features (for-est cover, hydrographic network), SAC was very strong at small spatial scales, but was positive and signifi cant also at larger scales (hydrographic network: up to 5000 m; for-est cover: up to 20 000 m). Land cover and hydrography are strongly related to topography and to the distribution of human activities at the regional scale, therefore strong SAC was not unexpected. For instance, the study area is dominated by hills and low elevation mountains; human activities are concentrated in lowlands and at the bottom of valleys, while at mid-elevations the hydrographic network is more dense and the landscape is dominated by forests. We observed signifi cant SAC also for more local features,

699

Table 2. Comparison of OLS logistic regression model with spatial eigenvector mapping integrating spatial autocorrelation using different approaches. All models included forest cover, length of hydrographic network and hydroperiod as independent variables. The OLS model is compared with three implementations of SEVM, built considering different distance matrices. For each model, we also report the amount of variation explained by environmental variables and spatial components.

% explained variation

χ 2 DF p AIC R 2 N E S J

a) OLS logistic regression 176.4 3 � 0.001 603.2 0.360 100 – –

b) spatial eigenvector mapping; variant: 30 eigenvectors-PCNMGabriel network 218.6 4 � 0.001 563.1 0.431 45 16 38Truncation distance:

200 m 233.1 4 � 0.001 548.5 0.454 63 21 16500 m 228.7 4 � 0.001 552.9 0.447 53 19 28750 m 213.8 4 � 0.001 567.8 0.423 51 15 341000 m 212.8 4 � 0.001 568.8 0.421 50 14 351500 m 219.2 4 � 0.001 562.4 0.432 41 17 422000 m 216.8 4 � 0.001 564.8 0.428 41 16 433000 m 221.1 4 � 0.001 560.5 0.435 41 17 41

c) spatial eigenvector mapping; variant: Moran ’ s I reduction-PCNMGabriel network 182.2 4 � 0.001 599.4 0.370 97 3 0Truncation distance:

200 m 181.4 4 � 0.001 600.2 0.369 92 2 5500 m 177.1 4 � 0.001 604.5 0.361 99 0 1750 m 180.9 4 � 0.001 600.7 0.368 96 2 21000 m 182.8 4 � 0.001 598.8 0.371 97 3 01500 m 183.2 4 � 0.001 598.5 0.372 96 3 12000 m 182.9 4 � 0.001 598.7 0.371 88 3 93000 m 182.2 4 � 0.001 599.4 0.370 85 3 13

d) spatial eigenvector mapping; variant: Moran ’ s I reduction-MEMGabriel network 179.6 4 � 0.001 602.3 0.366 98 2 0Truncation distance:

200 m 191.6 4 � 0.001 590.0 0.386 95 5 0500 m 180.6 4 � 0.001 601.0 0.367 98 2 0750 m 180.6 4 � 0.001 601.0 0.367 99 1 01000 m 185.2 4 � 0.001 596.4 0.375 96 4 01500 m 182.2 4 � 0.001 599.4 0.370 97 3 02000 m 183.0 4 � 0.001 598.6 0.371 83 3 143000 m 181.0 4 � 0.001 600.6 0.368 87 2 11

AIC: Akaike ’ s information criterion; R 2 N : Nagelkerke ’ s R 2 ; E: percentage of explained variation accounted for by the independent effect of environ-mental variables; S: explained variation accounted for by the independent effect of spatial eigenvectors; J: explained variation accounted for by the joint effect of environmental and spatial variables; PCNM: principal coordinates of neighbour matrices; MEM: Moran ’ s eigenvector maps.

such as microhabitat (morphological features of streams) and biotic communities (macrobenthos and periphyton) (Supplementary material Appendix 1, Fig. A1). Microhabitat parameters are strongly related to features like altitude, slope and geology; nearby sites are also usually part of the same watershed. Moreover, macrobenthos and periphyton are infl uenced by both exogenous environmental param-eters, which are in turn autocorrelated, and by endogenous parameters (such as dispersal) (McAbendoth et al. 2005). Th ere was an obvious correspondence between the SAC of the study species (Fig. 2a), and the SAC of environmen-tal features determining its distribution (Supplementary material Appendix 1, Fig. A1). Th is correspondence indi-cates that environmental factors aff ecting species distribu-tion also play a major role in the pattern of autocorrelation; in other words, most SAC of salamander distribution at large spatial scales can be described as exogenous.

Nevertheless, signifi cant residual autocorrelation rem-ained after taking into account the environmental variables. Residual SAC was signifi cant at distances up to 500 m (Fig.

2b – d), validating our a priori hypothesis that 500 m is the scale at which most fl ow of individuals occurs (Table 1, Glandt 1986). Alternative hypotheses are that residual SAC is caused by model misspecifi cation, such as lack of non-linear terms, or the lack of important endogenous fac-tors. However, these misspecifi cation hypotheses were not supported by the data. Th e pattern of residual SAC was nearly identical in the standard model, in GAM and in the model considering additional environmental variables, despite them explaining a very diff erent amount of varia-tion (OLS with 3 environmental variables: R 2 N � 0.36; GAM: R 2 N � 0.39; OLS with 6 environmental variables: R 2 N � 0.76), and despite the very diff erent sample size of the datasets (565 vs 132 sites), which consequently have diff erent statistical power. Even if it is always possible that our model is missing some predictor, the large amount of explained variation suggests that we included the most important relevant variables. Th erefore, our results strongly support the idea that SAC analysis can provide useful infor-mation on endogenous processes (McIntire and Fajardo

700

Figure 3. Spatial autocorrelation of eigenvectors extracted by diff erent implementations of spatial eigenvector mapping (SEVM). (a–g): SEVMs based on the matrix of geographic distances, assuming truncation distances (T) ranging from 200 to 3000 m. (h): SEVMs based on Gabriel network. Empty diamonds: ‘ 30 eigenvectors ’ variant; fi lled dots: ‘ Moran ’ s I reduction-PCNM ’ variant; empty triangles: ‘ Moran ’ s I reduction-MEM ’ variant. Error bars are twice the standard error of Moran ’ s I.

2009). Other studies used distribution data to evaluate the importance of dispersal processes in shaping populations and communities (Tuomisto et al. 2003, Chapman et al. 2009). For instance, Tuomisto et al. (2003) showed that environmental determinism and dispersal explain most of variation in Amazonian plant communities, but dispersal was more important for species that are poor dispersers. Th e strong residual autocorrelation of our data (Fig. 2b), and the improvement of model performance when spatial predictors are included (Table 2) are in agreement with these fi ndings, and support a relevant role of dispersal on the distribution of the study species (Chapman et al. 2009).

Th e analysis of eigenvectors extracted by SEVMs is an alternative approach to identify the scale of endogenous SAC. However, the results of this analysis were infl uenced by the various implementations used, with diff erences for both model fi t and autocorrelation of extracted eigenvectors. Th e 30 eigenvectors variant had consistently lower AIC val-ues and explained substantially more variation than the two Moran ’ s I reduction variants (Table 2). Th is is not surprising, as the 30 eigenvectors approach explicitly selects the com-bination of eigenvectors best describing the distribution of the study species, and combines them in a single variable, thereby minimizing the increase in AIC (Diniz-Filho et al. 2008), while the two Moran ’ s I reduction implementations

701

require the preservation of multiple, non isolated streams (Marsh and Trenham 2001, Lindenmayer and Fischer 2006). Other approaches (e.g. population genetics, direct observa-tions, analysis of occupancy and landscape features within concentric buff ers) have been used to identify population link-ages. SAC analysis can have some advantages compared to the other approaches. Large areas can be analysed faster and at a lower cost compared to population genetics, capture – mark – recapture or radiotracking. Furthermore, SAC analysis can explicitly incorporate environmental variables (e.g. habitat availability), which are aff ected by SAC and can have a con-founding eff ect on the analysis of concentric buff ers (Ficetola and De Bernardi 2004). Off course, SAC analysis has also limitations, because it does not provide direct information on the fl ow of individuals, and because of the risk of incorrect inference when not considering key predictors. Nevertheless, we believe that it can be a further tool available to conserva-tion managers, and it would provide very useful information, particularly when biologically relevant a priori hypotheses are evaluated, and when analyses are performed in conjunction with other approaches.

Acknowledgements – We thank Pedro Peres-Neto and four reviewers for insightful comments on early versions of the manuscript. GFF was funded by a scholarship of the Univ. degli Studi di Milano-Bicocca.

References

Angelone, S. and Holderegger, R. 2009. Population genetics suggests eff ectiveness of habitat connectivity measures for the European tree frog in Switzerland. – J. Appl. Ecol. 46: 879 – 887.

Bar-David, S. et al. 2007. Long-distance movements by fi re sala-manders ( Salamandra infraimmaculata ) and implications for habitat fragmentation. – Isr. J. Ecol. Evol. 53: 143 – 159.

Beale, C. M. et al. 2010. Regression analysis of spatial data. – Ecol. Lett. 13: 246 – 264.

Beguer í a, S. and Pueyo, Y. 2009. A comparison of simultaneous autoregressive and generalized least squares models for dealing with spatial autocorrelation. – Global Ecol. Biogeogr. 18: 273 – 279.

Betts, M. G. et al. 2009. Comment on “Methods to account for spatial autocorrelation in the analysis of species distributional data: a review”. – Ecography 32: 374 – 378.

Bini, L. M. et al. 2009. Coeffi cient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression. – Ecography 32: 193 – 204.

Bivand, R. 2010. spdep. Spatial dependence: weighting schemes, statistics and models. R package version 0.5 – 24. – � www.r-project.org � .

Borcard, D. and Legendre, P. 2002. All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. – Ecol. Model. 153: 51 – 68.

Burnham, K. P. and Anderson, D. R. 2002. Model selection and multimodel inference: a practical information-theoretic approach. – Springer.

Chapman, D. S. et al. 2009. Process from pattern in the distribu-tion of an endangered leaf beetle. – Ecography 32: 259 – 268.

Conlisk, E. et al. 2009. Improved abundance prediction from presence – absence data. – Global Ecol. Biogeogr. 18: 1 – 10.

Crump, M. L. and Scott, N. J. 1994. Visual encounter surveys. – In: Heyer, W. R. et al. (eds), Measuring and monitoring

aim at reducing autocorrelation only, without considering the amount of variation explained. A detailed comparison of the performance of 30 eigenvectors and Moran ’ s I reduction approaches, and the discussion of the causes of diff erences, is beyond the aims of this work (see Bini et al. 2009 for a comparison of SEVM variants). Nevertheless, when using the same distance matrix, in most of cases the pattern of autocorrelation of eigenvectors was similar among the three variants: SAC was very strong at distances � than the trunca-tion distances, and declined with some oscillations at larger distances (Fig. 3). In other words, SAC of eigenvectors was strongly determined by the a priori defi nition of the distance matrix used for the analysis (Dray et al. 2006), suggesting that the analysis of eigenvectors may be a non robust measure of the spatial scale at which autocorrelation actually takes eff ect. On the other hand, the eigenvectors of the SEVMs with best fi t ( ‘ 30 eigenvectors ’ variants assuming truncation distances of 200 – 500 m) (Dray et al. 2006) showed strong autocorrelation at scales up to 200 – 500 m (Fig. 3a, b), i.e. they suggest patterns similar to the ones obtained from the analysis of residual autocorrelation (Fig. 2) and further vali-date the dispersal hypothesis, formulated on the basis of the review of literature (Table 1). Finally, variance partitioning showed that, at large truncation distances, more variation was accounted for by the joint eff ect of environmental and spatial variables (Table 2). Th is suggests that, in our study system, analyses at the smallest truncation distances may be more appropriate to tease apart the eff ects of environmental and spatial variables. Nevertheless, simulations indicate that the results of variance partitioning of spatial datasets may be inaccurate, suggesting care in the interpretation of these results (Gilbert and Bennett 2010).

Th eoretical arguments suggest that it is impossible infer-ring with certitude endogenous population processes from spatial autocorrelation (van Teeff elen and Ovaskainen 2007, Dormann 2009). Nevertheless, distribution data can con-tain a signal of endogenous forces determining the cluster-ing of populations (van Teeff elen and Ovaskainen 2007), and the formulation of a priori, testable hypotheses can allow to understand processes on the basis of spatial patterns (McIntire and Fajardo 2009). Our approach can provide useful information when the major environmental variables determining species distribution are considered. It is clearly diffi cult to assess whether the model is missspecifi ed or some key predictor is lacking. Comparing models including dif-ferent sets of environmental variables and explaining diff er-ent amount of variation can help to assess the robustness of results.

Th e identifi cation of endogenous SAC can provide insights on population processes, and also provides important infor-mation for species management. Clusters of nearby locali-ties linked by dispersal can have higher probability of long term population persistence (Lindenmayer and Fischer 2006). Th erefore, managers can be interested in identifying the maximum distance among breeding localities that can be eff ectively linked. Our analysis identifi ed the distance among wetlands at which dispersal can signifi cantly aff ect occupancy: in this study case, approx. 500 m. Streams that are � 500 m apart from the nearest breeding sites are likely to be isolated; long term species conservation at the regional scale would

702

Joly, J. 1968. Donn é es é cologiques sur la salamandre tachet é e Salamandra salamandra . – Ann. Sci. Nat. Zool. 12: 301 – 366.

Kissling, W. D. and Carl, G. 2008. Spatial autocorrelation and the selection of simultaneous autoregressive models. – Global Ecol. Biogeogr. 17: 59 – 71.

Legendre, P. 1993. Spatial autocorrelation: trouble or new para-digm? – Ecology 74: 1659 – 1673.

Lichstein, J. W. et al. 2002. Spatial autocorrelation and autoregres-sive models in ecology. – Ecol. Monogr. 72: 445 – 463.

Liebhold, A. et al. 2004. Spatial synchrony in population dynam-ics. – Annu. Rev. Ecol. Evol. Syst. 35: 467 – 490.

Lindenmayer, D. B. and Fischer, J. 2006. Habitat fragmentation and landscape change. – Island Press.

Manenti, R. et al. 2009a. Habitat features and distribution of Salamandra salamandra in underground springs. – Acta Her-petol. 4: 143 – 151.

Manenti, R. et al. 2009b. Water, stream morphology and land-scape: complex habitat determinants for the fi re salamander Salamandra salamandra . – Amphibia-Reptilia 30: 7 – 15.

Marsh, D. M. and Trenham, P. C. 2001. Metapopulations dynam-ics and Amphibian conservation. – Conserv. Biol. 15: 40 – 49.

Mazzoleni, I. 2005. Importanza relativa di ambiente terrestre e acquatico per la distribuzione di Salamandra salamandra . – MSc thesis, Univ. degli studi di Milano.

McAbendoth, L. et al. 2005. Unravelling nestedness and spatial pattern in pond assemblages. – J. Anim. Ecol. 74: 41 – 49.

McIntire, E. J. B. and Fajardo, A. 2009. Beyond description: the active and eff ective way to infer processes from spatial patterns. – Ecology 90: 46 – 56.

N ö llert, A. and N ö llert, C. 1992. Die Amphibien Europas. – Kosmos.

Peres-Neto, P. R. and Legendre, P. 2010. Estimating and control-ling for spatial structure in the study of ecological communi-ties. – Global Ecol. Biogeogr. 19: 174 – 184.

Petersen, R. C. 1992. Th e RCE – a riparian, channel, and environ-mental inventory for small streams in the agricultural land-scape. – Freshw. Biol. 27: 295 – 306.

Rangel, T. F. L. V. B. et al. 2010. SAM: a comprehensive applica-tion for spatial analysis in macroecology. – Ecography 33: 46 – 50.

Rowe, G. and Beebee, T. J. C. 2007. Defi ning population bound-aries: use of three Bayesian approaches with microsatellite data from British natterjack toads ( Bufo calamita ). – Mol. Ecol. 16: 785 – 796.

Schulte, U. et al. 2007. A PIT tag based analysis of annual movement patterns of adult fi re salamanders ( Salamandra salamandra ) in a middle European habitat. – Amphibia-Reptilia 28: 531 – 536.

Siesa, M. E. et al. 2011. Spatial autocorrelation and the analysis of invasion processes from distribution data: a study with the crayfi sh Procambarus clarkii . – Biol. Invasions 13: 2147–2160.

Smith, M. A. and Green, D. M. 2005. Dispersal and the meta-population paradigm in amphibian ecology and conservation: are all amphibian populations metapopulations? – Ecography 28: 110 – 128.

Steinfartz, S. et al. 2000. Mitochondrial sequence analysis of Salamandra taxa suggests old splits of major lineages and postglacial recolonizations of central Europe from distinct source populations of Salamandra salamandra . – Mol. Ecol. 9: 397 – 410.

Tobler, W. R. 1970. Movie simulating urban growth in the Detroit region. – Econ. Geogr. (Suppl.) 46: 234 – 240.

Tuomisto, H. et al. 2003. Dispersal, environment, and fl oristic variation of western Amazonian forests. – Science 299: 241 – 244.

biological diversity: standard methods for Amphibians. Smith-sonian Inst. Press, pp. 84 – 92.

Degani, G. and Warburg, M. R. 1978. Population structure and seasonal activity of the adult Salamandra salamandra (L.) (Amphibia, Urodela, Salamandridae) in Israel. – J. Herpetol. 12: 437 – 444.

Deno ë l, M. 1996. Ph é nologie et domaine vital de la salamandre terrestre Salamandra salamandra terrestris (Amphibia, Caudata) dans un bois du Pays de Herve (Belgique). – Chaiers d’Ethol. 16: 291 – 306.

Di Cerbo, A. and Razzetti, E. 2004. Salamandra pezzata Salamandra salamandra (Linnaeus, 1758). – In: Bernini, F. et al. (eds), Atlante degli Anfi bi e dei Rettili della Lombardia. Provincia di Cremona, pp. 64 – 66.

Diniz-Filho, J. A. F. and Bini, L. M. 2005. Modelling geographical patterns in species richness using eigenvector-based spatial fi lters. – Global Ecol. Biogeogr. 14: 177 – 185.

Diniz-Filho, J. A. F. et al. 2008. Model selection and information theory in geographical ecology. – Global Ecol. Biogeogr. 17: 479 – 488.

Dormann, C. F. 2007a. Assessing the validity of autologistic regres-sion. – Ecol. Model. 207: 234 – 242.

Dormann, C. F. 2007b. Eff ects of incorporating spatial autocor-relation into the analysis of species distribution data. – Global Ecol. Biogeogr. 16: 129 – 138.

Dormann, C. F. 2009. Response to comment on “Methods to account for spatial autocorrelation in the analysis of species distributional data: a review”. – Ecography 32: 379 – 381.

Dormann, C. F. et al. 2007. Methods to account for spatial auto-correlation in the analysis of species distributional data: a review. – Ecography 30: 609 – 628.

Dray, S. et al. 2006. Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM). – Ecol. Model. 196: 483 – 493.

Ficetola, G. F. 2008. Impacts of human activities and predators on the nest success of the hawksbill turtle, Eretmochelys imbricata , in the Arabian Gulf. – Chelonian Conserv. Biol. 7: 255 – 257.

Ficetola, G. F. and De Bernardi, F. 2004. Amphibians in an human-dominated landscape: the community structure is related to habitat features and isolation. – Biol. Conserv. 119: 219 – 230.

Ficetola, G. F. and Deno ë l, M. 2009. Ecological thresholds: an assessment of methods to identify abrupt changes in species–habitat relationships. – Ecography 32: 1075 – 1084.

Ficetola, G. F. et al. 2009. Infl uence of landscape elements in ripar-ian buff ers on the conservation of semiaquatic amphibians. – Conserv. Biol. 23: 114 – 123.

Ficetola, G. F. et al. 2011a. Landscape – stream interactions and habitat conservation for amphibians. – Ecol. Appl. 21: 1272 – 1282.

Ficetola, G. F. et al. 2011b. Early assessment of the impact of alien species: diff erential consequences of an invasive cray-fi sh on adult and larval amphibians. – Divers. Distrib. 17: 1141–1151.

Gilbert, B. and Bennett, J. R. 2010. Partitioning variation in eco-logical communities: do the numbers add up? – J. Appl. Ecol. 47: 1071 – 1082.

Glandt, D. 1986. Die saisonalen Wanderungen der mittleu-rop ä ischen Amphibien. – Bonner Zool. Beitr ä ge 37: 211 – 228.

Goldwyn, E. E. and Hastings, A. 2008. When can dispersal syn-chronize populations? – Th eor. Popul. Biol. 73: 395 – 402.

Griffi th, D. A. and Peres-Neto, P. R. 2006. Spatial modelling in ecology: the fl exibility of eigenfunction spatial analyses. – Ecol-ogy 87: 2603 – 2613.

Hanski, I. and Gaggiotti, O. E. (eds) 2004. Ecology, genetics and evolution of metapopulations. – Elsevier.

703

Vos, C. C. et al. 2001. Genetic similarity as a measure for connec-tivity between fragmented populations of the moor frog ( Rana arvalis ). – Heredity 86: 598 – 608.

Wagner, H. H. and Fortin, M.-J. 2005. Spatial analysis of land-scape: concepts and statistics. – Ecology 86: 1975 – 1987.

Wood, S. N. 2006. Generalized additive models: an introduction with R. – Chapman and Hall.

van Teeff elen, A. J. A. and Ovaskainen, O. 2007. Can the cause of aggregation be inferred from species distributions? – Oikos 116: 4 – 16.

Vos, C. C. and Stumpel, A. H. P. 1996. Comparison of habitat-isolation parameters in relation to fragmented distribution pat-tern in the tree frog ( Hyla arborea ). – Landscape Ecol. 11: 203 – 214.

Supplementary material (Appendix E6483 at � www.oikosoffi ce.lu.se/appendix �). Appendix 1.