Electronic Supplementary Material s14

Electronic Supplementary Material

Age of the study trees

To assess the approximate age range of the study trees we took core samples from 20 trees at four sites that were widely dispersed in the study landscape. We randomly selected five trees at each site belonging to two size classes (two with dbh 50-75 cm and three with dbh 76-110 cm).

We calculated the annual growth rate for each tree as: (number of annual rings)/(length of the core sample). Next, we calculated the ages of the study trees based on their diameters, assuming the same annual growth rate for all trees.

Single variable tests

Table S1. Relationship (Rel; sign of parameter estimate) between single variables and lichen occurrence probability. ΔAIC = change in AIC when adding the variable to the null model. Si = connectivity. The Null model is a model with only the intercept.

Chaenotheca phaeocephal Chrysothrix Buellia Cliostomum a candelaris violaceofusca corrugatum Rel ΔAIC Rel ΔAIC Rel ΔAIC Rel ΔAIC Bark fissure depth + 1.5 + -9.5 + 1.3 + -6.5 Tree diameter + 0.6 + -0.7 - 2.0 + -2.7 Shade - -0.9 + -5.8 - 2.0 - 1.9 Bush cover - -10.6 + 0.0 - 1.6 + 2.0 Macrolichen cover - 1.7 - 1.8 - 2.0 - -2.1 Wind exposure + -7.4 - 1.2 + 1.9 - 2.0 Moss cover - -0.2 + -0.3 - 1.9 - 1.8 Distance to field + 0.6 - 2.0 + -0.4 - 1.8 Inclination + 1.9 + 2.0 - 1.9 - 2.0

Si 1830 + -0.2 + -4.2 + -16.2 + 0.3

Si 2009 - 2.5 + 2.7 + -2.3 + 3.1 AIC Null model 109.3 91.3 47.9 53.3

1 Alternative models

Table S2. Parameter estimates and AIC of the final models (in bold) and plausible alternative models for the occurrence probability of the four lichen species.

Species Intercept Bark Diameter Shade Bush cover Wind Si 2009 Si 1830 AIC fissure exposure depth Chaenotheca 0.99 (0.32) -0.78 (0.24) 1.52 (0.65) 0.45 (0.29) 93.3 phaeocephal a 0.94 (0.31) -0.71 (0.23) 1.52 (0.64) 94.0 1.49 (0.28) -0.86 (0.25) 0.45 (0.28) 97.8 0.77 (0.29) 1.66 (0.60) 0.31 (0.25) 102.4

Chrysothrix 2.65 (0.51) 1.26 (0.50) 1.20 (0.37) 0.87 (0.43) 73.3 candelaris 2.41 (0.46) 1.39 (0.48) 1.14 (0.35) 74.7 2.20 (0.39) 0.87 (0.33) 1.05 (0.43) 80.5 2.17 (0.40) 0.77 (0.83) 0.83 (0.42) 84.8

Buellia -5.44 (1.55) 2.63 (0.91) 29.7 violaceofusca -3.31 (0.62) 1.06 (0.46) 45.6

Cliostomum -3.13 (0.55) 1.04 (0.38) 46.8 corrugatum -2.96 (0.51) 0.88 (0.43) 50.6

2 The study landscape

Fig. S1 The study landscape in south-eastern Sweden. Black dots represent the 104 study trees, and the grey scale shows the number of oaks in 50 × 50 m cells based on oak densities in 1830 and 2009, in 63 villages. The black line indicates the outer margin of a 1.8 km buffer zone.

3 Code for estimating α and its 95% confidence interval in R

Ntrees = 104 # Number of study trees

Ncells = 4048 # Number of 50 x 50 m cells within 1800 m

Connmat = matrix(nrow = Ntrees, ncol = Ncells) # Connectivity matrix

# PresAbs is species presence/absence and d[i,j] is the distance in metres between the

# centre of cell i where the focal oak is located and the centre of cell j. A[i,j] is # the number of oaks in cell j for tree i.

# Optimizing alpha alphaopt <- function(alpha, A, PresAbs, dij){ # Optimization function for α

for(i in 1:Ntrees){ # Loop for trees

for(j in 1:Ncells){ # Loop for cells

Connmat[i,j] <- exp(- alpha * d[i,j])* A[i,j] # The contribution for each cell

Si[i] <- sum(Connmat[i,]) # Connectivity

# Generalized linear model mod = glm(PresAbs~ Si, family = binomial(link = "logit")) deviance(mod)

# optimizing alphaopt opt.alpha <- optimize(alphaopt, c(0,0.1), d = d, PresAbs = PresAbs, A = A) best.alpha = opt.alpha[1][[1]] # α for the best model fit low.dev = opt.alpha[2][[1]] # Deviance for the best model

# The deviance profile and estimating the 95% confidence interval of α alpha = seq(0,0.1,0.0001) # 1001 alpha values ranging 0-0.1 dev = numeric(length(alpha)) # Vector for model deviance for(k in 1:length(alpha)){ # Loop for alphas

for(i in 1:Ntrees){ # Loop for trees

for(j in 1:Ncells){ # Loop for cells

4 Connmat[i,j] <- exp(- alpha[k] * d[i,j])* A[i,j]# The contribution for each cell

Si[i] <- sum(Connmat[i,]) # Connectivity

# Deviance of the generalized linear model dev[k] = deviance(glm(PresAbs ~ Si, family = binomial(link = "logit")))

} plot(alpha,dev) # Plot the deviance profile

# Lower and upper 95% confidence limits low95 = alpha[which.min(abs(dev[1:low.dev]-(dev[low.dev]+3.84)))] upp95 = alpha[which.min(abs(dev[low.dev:length(dev)]-(dev[low.dev]+3.84)))+low.dev-1]

# Test for spatial autocorrelation with variogram models

# Creating an empirical variogram mod.resid <- residuals(mod, type="pearson") # Model residuals empir.vario <- variog(coords=cbind(Xcoord, Ycoord), data=as.vector(mod.resid),

uvec=seq(0,500, l=30))

# Fitting a variogram model vario.pars.ML<- likfit(coords=cbind(Xcoord, Ycoord),

data=as.vector(mod.resid), ini.cov.pars=c(1, 500), cov.model="exponential") summary(vario.pars.ML)

# Computing and plotting variogram envelopes env.data = cbind(Xcoord, Ycoord, PresAbs) geo.data = as.geodata(env.data, coords.col = 1:2, data.col = 3) # Geodata object vario.env <- variog.model.env(geodata = geo.data, obj.variog = empir.vario,

coords = cbind(Xcoord, Ycoord), model.pars = vario.pars.ML, nsim=99) plot(empir.vario, env = vario.env, xlab = "Distance") lines(step.obt.vario.pars.ML)