DESCRIPTION OF THE DATASETS FOR THE SIMULATION STUDY SIMULATED DATASETS: zj_wheaters_100simul_marrays_immfix_sample1 100 simulated datasets and underlying demographic parameters where the number of immigrants is fixed and the sample size is the "natural" sample size. zj_wheaters_100simul_marrays_immfix_sample10 100 simulated datasets and underlying demographic parameters where the number of immigrants is fixed and the sample size is 10 times the "natural" sample size. zj_wheaters_100simul_marrays_immvary_sample1 100 simulated datasets and underlying demographic parameters where the number of immigrants varies "moderately" and the sample size is the "natural" sample size. zj_wheaters_100simul_marrays_immvary_sample10 100 simulated datasets and underlying demographic parameters where the number of immigrants varies "moderately" and the sample size is 10 times the "natural" sample size. zj_wheaters_100simul_marrays_immvary0.4_sample1 100 simulated datasets and underlying demographic parameters where the number of immigrants varies "strongly" and the sample size is the "natural" sample size. zj_wheaters_100simul_marrays_immvary0.4_sample10 100 simulated datasets and underlying demographic parameters where the number of immigrants varies "strongly" and the sample size is 10 times the "natural" sample size. For each of these datasets (simdata$) N: true yearly number of breeders N.TOT.sim: yearly number of breeders counted Nimm: yearly number of immigrants nfledg: yearly number of fledglings per brood fledg.nb.sim: yearly number of fledglings observed fledg.sample: yearly number of nests monitored (given as data, not simulated) phi: yearly survival rate for juveniles (phi[1,,,1]) and adults (phi[2,,,1]) marray.a.sim: capture recapture data for the adults in an m-array format marray.j.sim: capture recapture data for the juveniles in an m-array format r.a: number of adults marked each year (given as data, not simulated) r.j: number of juveniles marked each year (given as data, not simulated) nyears: number of years of the time series (24) POSTERIOR SAMPLES FROM IPMs FITTED TO SIMULATED DATASETS: zj_wheatear_IPM_sample1_immfix_Poisson posteriors from "IPMpois" parameterisation fitted to simulated data where the number of immigrants is fixed and the sample size is the "natural" sample size. zj_wheatear_IPM_sample1_immfix_noconstr posteriors from "IPMnoconst" parameterisation fitted to simulated data where the number of immigrants is fixed and the sample size is the "natural" sample size. zj_wheatear_IPM_sample1_immvary_Poisson posteriors from "IPMpois" parameterisation fitted to simulated data where the number of immigrants varies "moderately" and the sample size is the "natural" sample size. zj_wheatear_IPM_sample1_immvary_noconstr posteriors from "IPMnoconst" parameterisation fitted to simulated data where the number of immigrants varies "moderately" and the sample size is the "natural" sample size. zj_wheatear_IPM_sample1_immvary_0.4_Poison posteriors from "IPMpois" parameterisation fitted to simulated data where the number of immigrants varies "strongly" and the sample size is the "natural" sample size. zj_wheatear_IPM_sample1_immvary_0.4_noconstr posteriors from "IPMnoconst" parameterisation fitted to simulated data where the number of immigrants varies "strongly" and the sample size is the "natural" sample size. zj_wheatear_IPM_sample10_immfix_Poisson posteriors from "IPMpois" parameterisation fitted to simulated data where the number of immigrants is fixed and the sample size is 10 times the "natural" sample size. zj_wheatear_IPM_sample10_immfix_noconstr posteriors from "IPMnoconst" parameterisation fitted to simulated data where the number of immigrants is fixed and the sample size is 10 times the "natural" sample size. zj_wheatear_IPM_sample10_immvary_Poisson posteriors from "IPMpois" parameterisation fitted to simulated data where the number of immigrants varies "moderately" and the sample size is 10 times the "natural" sample size. zj_wheatear_IPM_sample10_immvary_noconstr posteriors from "IPMnoconst" parameterisation fitted to simulated data where the number of immigrants varies "moderately" and the sample size is 10 times the "natural" sample size. zj_wheatear_IPM_sample10_immvary_0.4_Poison posteriors from "IPMpois" parameterisation fitted to simulated data where the number of immigrants varies "strongly" and the sample size is 10 times the "natural" sample size. zj_wheatear_IPM_sample10_immvary_0.4_noconstr posteriors from "IPMnoconst" parameterisation fitted to simulated data where the number of immigrants varies "strongly" and the sample size is 10 times the "natural" sample size. For each of these sets of posterior samples (zj$) N: yearly number of breeders n: initial population size Nimm: yearly number of immigrants mean.Nimm: expected yearly number of immigrants mu.imm: mean number of immigrants (on the log scale) sigma.imm: temporal standard deviation of the number of immigrants (on the log scale) nfledg: yearly number of fledglings per brood mu.nfledg: mean number of fledglings per brood (on the log scale) sigma.nfledg: temporal standard deviation of the number of fledglings per brood (on the log scale) p.females: recapture probability phi: yearly survival rate for juveniles (phi[1,,,1]) and adults (phi[2,,,1]) eta.phi.females: mean survival rate of juveniles ([1,...]) and adults ([2,...]) (on the logit scale) sigma.phi.females: temporal standard deviation of the survival rate for juveniles and adults (on the logit scale) DESCRIPTION OF THE DATASETS FOR THE REAL CASE STUDIES Contribution_kestrel_poisson Contains the posteriors for the yearly number of immigrants (N.imm), yearly population growth rate (lam), transcient LTRE contribution of immigration rate (cont_Imm) and total LTRE contribution of all parameters (cont_tot) from the IPM with "poisson" parameterisation fitted on the Kestrel dataset Contribution_kestrel_noconstr Contains the posteriors for the yearly number of immigrants (N.imm), yearly population growth rate (lam), transcient LTRE contribution of immigration rate (cont_Imm) and total LTRE contribution of all parameters (cont_tot) from the IPM with "noconst" parameterisation fitted on the Kestrel dataset Contribution_sheep_poisson Contains the posteriors for the yearly number of immigrants (N.imm), yearly population growth rate (lam), transcient LTRE contribution of immigration rate (cont_Imm) and total LTRE contribution of all parameters (cont_tot) from the IPM with "poisson" parameterisation fitted on the Sheep dataset Contribution_sheep_noconstr Contains the posteriors for the yearly number of immigrants (N.imm), yearly population growth rate (lam), transcient LTRE contribution of immigration rate (cont_Imm) and total LTRE contribution of all parameters (cont_tot) from the IPM with "noconst" parameterisation fitted on the Sheep dataset Contribution_wolf_poisson Contains the posteriors for the yearly number of immigrants (N.imm), yearly population growth rate (lam), transcient LTRE contribution of immigration rate (cont_Imm) and total LTRE contribution of all parameters (cont_tot) from the IPM with "poisson" parameterisation fitted on the Wolf dataset Contribution_wolf_noconstr Contains the posteriors for the yearly number of immigrants (N.imm), yearly population growth rate (lam), transcient LTRE contribution of immigration rate (cont_Imm) and total LTRE contribution of all parameters (cont_tot) from the IPM with "noconst" parameterisation fitted on the Wolf dataset DESCRIPTION OF THE DATASETS FOR THE WHEATEAR POPULATION PROVIDED AS EXAMPLE FOR THE PROCEDURE DESCRIBED IN APPENDIX 6 data_wheatears Dataset from the Wheatear population near Uppsala, Sweden, used as example. The description of the data is the same as above for the simulation study: N.TOT: yearly number of breeders counted fledg.nb: yearly number of fledglings observed fledg.sample: yearly number of nests monitored marray.a: capture recapture data for the adults in an m-array format marray.j: capture recapture data for the juveniles in an m-array format r.a: number of adults marked each year r.j: number of juveniles marked each year nyears: number of years of the time series (24) model_realdata IPM fitted on the Wheatear data. All parameters are described above.