Appendix 1. Summary of Banding Data Used in Hierarchical Bayes Stopover Models

APPENDIX 1. – SUMMARY OF BANDING DATA USED IN HIERARCHICAL BAYES STOPOVER MODELS

Total annual number of individuals banded at Long Point Bird Observatory between 1987-2007 that were included in each of the species- and season-specific mark-recapture datasets, and the average annual total for each; data from 1993 and 2003 were excluded from analyses (NA).

Species Season 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2003 2002 2004 2005 2006 2007 Average

Temperate migrants HETH spring 187 90 220 159 114 73 NA 84 90 102 102 151 157 161 131 NA 113 110 132 193 147 132 fall 168 196 183 125 107 99 NA 112 316 138 155 223 149 202 230 NA 170 132 147 211 93 166 RCKI spring 471 218 332 382 461 116 NA 281 227 152 147 256 211 290 158 NA 235 179 214 276 250 256 fall 690 450 483 853 519 285 NA 341 590 276 329 379 429 731 487 NA 444 510 700 695 413 505 DEJU spring 48 72 92 74 177 134 NA 76 37 40 134 69 49 21 90 NA 53 43 90 55 57 74 fall 59 53 78 165 94 58 NA 74 46 99 121 107 72 150 80 NA 152 72 97 289 105 104 WTSP spring 362 210 298 309 442 436 NA 323 216 176 299 379 371 498 422 NA 533 728 379 484 828 405 fall 123 145 191 358 167 172 NA 137 202 201 203 169 139 327 378 NA 356 292 402 428 355 250

Tropical migrants AMRE spring 33 72 60 40 54 76 NA 41 54 47 94 44 63 59 33 NA 57 35 62 34 69 54 fall 90 47 68 62 88 51 NA 101 75 76 69 115 46 81 64 NA 70 50 43 110 98 74 BTBW spring 22 39 27 18 29 40 NA 19 66 44 55 21 75 61 41 NA 30 31 47 31 53 39 fall 52 32 42 47 55 24 NA 33 100 59 40 94 85 54 77 NA 95 69 66 94 81 63 MAWA spring 408 274 229 280 232 209 NA 141 283 175 268 280 323 333 304 NA 176 175 273 297 295 261 fall 158 101 138 130 201 85 NA 120 200 157 102 129 144 113 129 NA 176 109 90 225 138 139 SWTH spring 11 69 43 49 39 61 NA 32 41 49 74 54 49 61 59 NA 44 55 61 64 83 53 fall 148 216 210 112 196 103 NA 58 176 75 144 180 121 145 121 NA 127 84 329 145 242 154

1 APPENDIX 2. – BUGS CODE FOR THE MIGRATORY STOPOVER MODEL WITH A LINEAR COVARIATE

BUGS code for a hierarchical stopover-decision model with annual climate covariate { phi[NAO*k] p[y*k] Psi[y*k] } where parameters are constrained for all but one state (the “non-transient state”, see text and Schaub et al. 2004). Note that to be consistent with standard mark-recapture notation and other related models, this code uses phi for the ’survival’ parameter (denoted ε in the manuscript), and Psi for the ’transition’ parameter (denoted τ in the manuscript). Parameter phi is constrained to vary as a linear function of annual NAO index, while parameters p and Psi are all allowed to vary across years (y) and among states (k). Within the multi-state stopover model encounter history data, individuals were assigned a value of 1 (initial state) at their first encounter, and 2 (non-transient state) at every subsequent encounter; all other days were denoted by a 4 (no observation for that individual; denoted by 0 in traditional mark-recapture), as individuals in state 3 (transients) are by definition unobservable following initial capture. For further details on parameter definitions, model structure and development, and notation for the more general model (without a climate covariate), see Calvert et al. (2009b).

# model { phi[yk] p[NAO*k] Psi[yk] } for K=3 (dead/unobserved =4), with stopover constraints

# data file requirements: K (number of states), Bidx[y] (limit of data for each year y), idx[i] (beginning and end-point of encounter histories for each individual i), z[t] (vector of true states at each time t), w[t] (observation indication vector at each time t), c[i] (initial capture date for individual i), NAO[y] (NAO index value for each year y) # initial values file requirements: z[t], etap, etaphi, etaPsi, etaBp, etaBPsi, b0, b1, mu.p[k], mu.Psi[k] model {

# Hyper-priors on phi, Psi and p

mu.p ~ dnorm(0,0.667) tau.p ~ dgamma(0.001,0.001)

### Need to put priors on the slope/intercept of NAO effect (b0, b1) instead of the mean (mu.phi) b0 ~ dnorm(0, 0.667) b1 ~ dnorm(0, 0.667) I(-2,2) tau.phi ~ dgamma(0.001,0.001)

mu.Psi ~ dnorm(0,0.667) tau.Psi ~ dgamma(0.001,0.001)

# calculate hierarchical means for year-variant parameters: reverse log-transform of hyperpriors mean.p <- exp(mu.p) / (1+exp(mu.p)) mean.Psi <- exp(mu.Psi) / (1+exp(mu.Psi))

# Bayes predictive distributions for year-variant parameters (p & Psi)

logit(Bpd.p) <- etaBp etaBp ~ dnorm(mu.p, tau.p)

logit(Bpd.Psi) <- etaBPsi etaBPsi ~ dnorm(mu.Psi, tau.Psi)

# loop over years for (y in 1:Y){

# Priors on p, phi & Psi in each state (with specific stopover constraints and NAO effect on phi)

2 p[y,1] <- 0 logit(p[y,2]) <- etap[y] etap[y] ~ dnorm(mu.p, tau.p) I(-4,4) p[y,3] <- 0 p[y,K+1] <- 0

phi[y,1] <- 1 logit(phi[y,2]) <- etaphi[y] mu.phi[y] <- b0 + b1*(NAO[y]) # NAO effect on (1-departure probability) etaphi[y] ~ dnorm(mu.phi[y], tau.phi) I(-4,4) phi[y,3] <- 0

Psi[y,1,1] <- 0 logit(Psi[y,1,2]) <- etaPsi[y] etaPsi[y] ~ dnorm(mu.Psi, tau.Psi) I(-4,4) Psi[y,1,3] <- 1-Psi[y,1,2] # transient probability

Psi[y,2,1] <- 0 Psi[y,2,2] <- 1 Psi[y,2,3] <- 0

Psi[y,3,1] <- 0 Psi[y,3,2] <- 0 Psi[y,3,3] <- 1

# defining "transition" probability q (surviving and moving in one time step) among states

q[y,K+1, K+1] <- 1

for (k in 1:K){ q[y,K+1, k] <- 0 q[y,k, K+1] <- 1 - phi[y,k]

for (j in 1:K){ q[y,k,j] <- phi[y,k] * Psi[y,k,j] } # close j loop } # close k loop

# defining likelihoods and relationships between data and process

for (i in Bidx[y]:(Bidx[y+1]-1)){ for (t in (idx[i]+c[i]):(idx[i+1]-1)){

# Process model z[t] ~ dcat(q[y,z[t-1],1:K+1])

# Observation model w[t] ~ dbern(p[y,z[t]])

} # close t loop

} # close i loop

} # close y loop

} # end of model

3 APPENDIX 3 – ANNUAL ESTIMATES OF TRANSIENCE AND DEPARTURE AT STOPOVER FOR EIGHT SPECIES OF MIGRANTS AT LONG POINT, ONTARIO.

Hermit thrush (Catharus guttatus; HETH); temperate migrant - spring (top) and fall (bottom) estimates of transience (left) and departure (right) at Long Point, Ontario from 1987-2007 (missing values for 1993, 2003), and hierarchical mean (Hm), from a hierarchical Bayes multi- state mark-recapture model.

4 Ruby-crowned kinglet (Regulus calendula; RCKI); temperate migrant - spring (top) and fall (bottom) estimates of transience (left) and departure (right) at Long Point, Ontario from 1987-2007 (missing values for 1993, 2003), and hierarchical mean (Hm), from a hierarchical Bayes multi-state mark-recapture model.

5 Dark-eyed junco (Junco hyemalis; DEJU); temperate migrant - spring (top) and fall (bottom) estimates of transience (left) and departure (right) at Long Point, Ontario from 1987-2007 (missing values for 1993, 2003), and hierarchical mean (Hm), from a hierarchical Bayes multi- state mark-recapture model.

6 White-throated sparrow (Zonotrichia albicollis; WTSP); temperate migrant - spring (top) and fall (bottom) estimates of transience (left) and departure (right) at Long Point, Ontario from 1987-2007 (missing values for 1993, 2003), and hierarchical mean (Hm), from a hierarchical Bayes multi-state mark-recapture model.

7 American redstart (Setophaga ruticilla; AMRE); tropical migrant - spring (top) and fall (bottom) estimates of transience (left) and departure (right) at Long Point, Ontario from 1987-2007 (missing values for 1993, 2003), and hierarchical mean (Hm), from a hierarchical Bayes multi- state mark-recapture model.

8 Black-throated blue warbler (Dendroica caerulescens; BTBW); tropical migrant - spring (top) and fall (bottom) estimates of transience (left) and departure (right) at Long Point, Ontario from 1987-2007 (missing values for 1993, 2003), and hierarchical mean (Hm), from a hierarchical Bayes multi-state mark-recapture model.

9 Magnolia warbler (Dendroica magnolia; MAWA); tropical migrant - spring (top) and fall (bottom) estimates of transience (left) and departure (right) at Long Point, Ontario from 1987-2007 (missing values for 1993, 2003), and hierarchical mean (Hm), from a hierarchical Bayes multi-state mark-recapture model.

10 Swainson’s thrush (Catharus ustulatus; SWTH); tropical migrant - spring (top) and fall (bottom) estimates of transience (left) and departure (right) at Long Point, Ontario from 1987-2007 (missing values for 1993, 2003), and hierarchical mean (Hm), from a hierarchical Bayes multi-state mark-recapture model.