Ecological Archives E094-217-A4

Tamar Lok, Otto Overdijk, Joost M. Tinbergen, Theunis Piersma. 2013. Seasonal variation in density dependence in age-specific survival of a long-distance migrant. Ecology 94:2358–2369.

Appendix D. Population matrix model to predict population growth.

We investigated whether the estimated annual variation in survival, in combination with the estimated change in fidelity, could predict the observed pattern of population growth. For this, we used the shrunken estimates of age-specific survival from the best-supported random effects models per age class (Nquad, σ² for S0 and Nlin, σ² for S1, S2 and S≥3) and the maximum likelihood estimates of fidelity (estimates shown in Table B3). We applied the following pre-breeding census based age-structured population matrix model (Caswell 2001):

Nx reflects the number of female birds in age class x and f is the average number of female offspring produced per adult (≥3 year old) female bird. Within the adult age class, breeding propensity was assumed to be independent of age and constant over years. The population size in 1991 was used as the starting population size (consisting of 527 breeding pairs, i.e., 527 females) and was assumed to have the stable age structure calculated from the Leslie matrix with the estimates of vital rates in 1991. Calculations were performed using the popbio package (Stubben and Milligan 2007) in program R (version 2.13.0, R Development Core Team 2011).

Literature cited

Caswell, H. 2001. Matrix population models: construction, analysis and interpretation, Second edition. Sinauer Associates, Sunderland, Massachusetts, USA.

Stubben, C., and B. Milligan. 2007. Estimating and analyzing demographic models using the popbio package in R. Journal of Statistical Software 22:1–23.

R Development Core Team. 2011. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.

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