The goal was to estimate the relationship between population connectedness and the composition of the landscape between populations. For the purposes of this study, a “population” was defined as the set of individuals breeding within a discrete wetland. The study had three stages: (1) the extent of dispersal among pairs of habitat patches was inferred indirectly from estimates of genetic divergence using neutral microsatellite markers; (2) the composition of the landscape between pairs of patches was measured from detailed maps of the study area; and (3) the relative contributions of types of landscape elements to population divergence were estimated using linear models. A strength of my approach is that information on resistance of landscape features to dispersal comes entirely from the organisms themselves. There was no initial step, as implemented in many other studies, of judging landscape permeability based on natural history information, behavioral observations, or expert opinion (e.g., Ray et al. 2002; Adriaensen et al. 2003; Cushman et al. 2006; Stevens et al. 2006; Compton et al. 2007; Storfer et al. 2007, 2010).
The habitat patches were wetlands supporting breeding aggregations of the common frog (R. temporaria) and alpine newt (T. alpestris), within an 800-km2 region of northern Switzerland (Fig. 1; Table S1). I studied only some of the many amphibian breeding localities within this region, chosen because of their accessibility for sampling or because I was able to secure permits for them. Unsampled populations do not severely bias estimates of migration rate among the sampled populations, according to Beerli's (2004) simulations, although Slatkin (2005) cautions that so-called “ghost populations” can be important under some circumstances.
Neutral genetic samples
For R. temporaria, I collected one fertilized egg from each of at least 20 different clutches in each of 48 ponds in March 2000; 996 embryos were collected in total. Insofar as possible, half-sibs sired by the same male were avoided by sampling from clutches of different ages and in different parts of the pond. After tadpoles hatched and resorbed the yolk sac, they were stored in 96% ethyl alcohol until the DNA was extracted. The number of individuals genotyped per population averaged 20.7 (range 13–36; three populations had <17 samples). For T. alpestris, samples came from 816 larvae collected in 41 ponds by dip-netting or pipe-sampling during July 2000 (Van Buskirk 2009). Again, I avoided sampling relatives by distributing the dip-nets or pipe throws across large areas of the pond. The number of individuals per population averaged 19.9 (range 6–53). Tissue samples were stored in alcohol.
Amphibian larvae were genotyped at highly variable microsatellite loci, applying previously described protocols (Garner et al. 2003). There were eight loci for R. temporaria and seven loci for T. alpestris. One R. temporaria locus showed evidence for divergent selection, according to the test of Beaumont and Nichols (1996), and was therefore discarded from analyses. The markers and their statistical properties are described in Tables S2 and S3; Fig. S1 for R. temporaria, and in Garner et al. (2003), Table S4; Fig. S1 for T. alpestris. Both species exhibited some significant deviations from Hardy–Weinberg equilibrium, using exact probability tests (Raymond and Rousset 1995). Therefore, I estimated the frequency of null alleles following Brookfield (1996, eq. 2) and included the estimated frequencies as a single allele in subsequent analyses. Estimated null allele frequency averaged 0.084 for R. temporaria and 0.065 for T. alpestris (Tables S2 and S4).
Landscape features were measured along straight-line dispersal paths and within lens-shaped regions connecting all pairs of populations within 10 km of each other. I did not include population pairs >10 km apart for several reasons. First, evidence suggests that amphibians are philopatric or usually disperse a few hundred meters between the larval stage and first reproduction, only rarely covering kilometers (reviewed in Smith and Green 2005). In addition, there was significant isolation by distance in both species (Fig. S2). This implies that more distant population pairs, generally more than 5–10 km apart, were connected by dispersal only indirectly and over longer periods of time. Thus, there is a greater risk that mutation contributes to divergence between more distant populations. Finally, barriers and land cover become less relevant as distance increases and large numbers of different types of barriers accumulate (Murphy et al. 2010; Jaquiery et al. 2011).
For every allowed dispersal path, I measured the overall straight-line distance and the surface area of a lens-shaped region having a width 20% of the length and the ends anchored at the pair of ponds. For the lens regions, the density of distinct ponds and building structures was recorded. For the straight-line paths, I measured distances passing through three types of land cover: forest, open field, and urban (density of building structures ≥10 ha−1). I also counted the number of times the dispersal path traversed a secondary road, a divided highway, a river >5-m wide, an airport runway, or a rail line. These habitat and barrier types were chosen because distinctions among them have proven important in earlier work on amphibians (Angelone et al. 2011; Hether and Hoffman 2012). The landscape data were measured from digital versions of 1:25,000 topographic maps, updated between 1998 and 2003 (Bundesamt für Landestopographie, Wabern, Switzerland). Older maps confirm that, while land cover on the study area is not unchanged in recent decades, the basic configuration of ponds, forests, roads, and urban areas has remained consistent since the 1970s. This is especially true for forests, which are protected by Swiss federal law.
Analyses described below assume that animals follow (nearly) linear dispersal paths between breeding sites, a common assumption in landscape genetics (Storfer et al. 2010). Although linear dispersal cannot really occur, highly directed movement in the terrestrial habitat is often observed in radio-telemetry studies of amphibians (Matthews and Pope 1999; Freidenfelds et al. 2011) and linear dispersal is supported by statistical modeling (Spear et al. 2005; Goldberg and Waits 2010). In any case, comparison among indirect dispersal paths requires independent information about resistance of landscape elements (e.g., “least-cost modeling”; Adriaensen et al. 2003), and this would be incompatible with my aim of estimating resistance directly from data on gene flow.
Interpopulation differentiation was estimated by FST using the allele identity method (Hardy and Vekemans 2002). FST is appropriate for this study because it indirectly reflects long-term migration rates between pairs of populations, under the assumption that divergence is more strongly influenced by drift than by selection and mutation (Slatkin 1991; Epperson 2005; Whitlock 2011). Although genetic effective population sizes (Ne) are not known, annual counts of the number of clutches produced by female R. temporaria between 1999 and 2011 were fairly small (median 121, range 11–2315, N = 48 ponds). This suggests that drift may be more important for population divergence than mutation (Crow and Aoki 1984). Moreover, private alleles were infrequent (0.0012 in R. temporaria and 0.0046 in T. alpestris), and this too implies that divergence was not primarily due to new mutations. For both species, genetic divergence was far too low to directly estimate first-generation migrants (e.g., Beerli and Felsenstein 2001).
The number of individuals dispersing between each pair of populations per generation, m, was estimated according to Slatkin's (1993, eq. 6) formulation for two populations: Nem = (1/FST − 1)/4. Although the value of Ne is unknown, specific information on Ne would influence estimates of absolute dispersal, but not the relative impacts of landscape features on gene flow (see 'Discussion').
For each species, I constructed three types of linear model. The first predicted gene flow among population pairs based on the distance within the dispersal path covered by forest (LF), open field (LO), and urban (LU) land covers. The parameters of this model reflect the relative resistances to gene flow of the three kinds of land cover. The number of migrants between two populations, i and j, was expressed as:
for all i < j (i.e., each population pair was included once). Mij is the logarithm of Nem; α is the intercept, which estimates gene flow between immediately adjacent populations; the βs are coefficients representing the impact of a 1-km length of forest, open, or urban land; and ε is the variation in Mij not explained by distances through the three land types.
The second model estimated the impact of discrete landscape elements – rivers, secondary roads, and highways – suspected to affect movement among populations:
where the intercept α estimates gene flow between ponds that are immediately adjacent and have no landscape elements separating them; Lij is the distance between populations i and j (km) (for all i < j); NR, NS, and NH are the number of rivers, secondary roads, and divided highways falling between the populations; βD is the change in gene flow per km; and the other βs are coefficients representing the impact of a single landscape element of the corresponding type. Railroad lines were combined with secondary roads and airport runways were combined with divided highways, because neither of these elements was sufficiently frequent to allow their contributions to be estimated separately. Convergence issues prevented me from including landscape elements and land cover within the same model, probably because multiple pairs of independent variables were highly correlated.
The third model asked whether gene flow was related to the densities of discrete building structures and wetlands falling within the lens-shaped region connecting pairs of populations:
where α is the intercept, Aij is the area of the lens-shaped region between populations i and j (ha); DB and DP are the densities of buildings and ponds falling within the lens-shaped area (per ha); βA is the change in gene flow for each 1-ha increase in the area of the lens region; and the other βs are coefficients representing the impact of a change in the density of buildings and ponds.
These analyses were inspired by that in Ricketts (2001), modified here for use with data on neutral marker divergence. Parameters were estimated by maximum likelihood in SAS version 9.2 (SAS Institute 2009); confidence intervals and significance were evaluated from 9,999 permutations of the response variables in eqs (1)-(3).