Giacomo Tavecchia, Eduardo Minguez, Ana de León, Maite Louzao, and Daniel Oro. 2008. Living close, doing differently: small-scale asynchrony in demography of two species of seabirds. Ecology 89:77–85.

Appendix C. Species- and colony-specific population matrix models.

Species- and colony-specific survival and fecundity parameters could be combined in a deterministic population matrix model for each of the four colonies (see below) as:

where, V^j, is the age-dependent vectors of individuals in the colony j at time i and A is the transition matrix containing the demographic parameters of colony j at time i (Caswell 2001).

We define:

F = number of fledglings

J^1st = number of 1^st year birds

J^2nd = number of 2 year old birds

A = number of adults

S^j_i = Survival between year i and i+1 for birds born in colony j (age-invariant). When considered constant over time we used the subscript "."

B^j_i = Adult breeding success in i for birds breeding in colony j (age-invariant)

sr = Proportion of female fledgling

The values of S^j_i, and B^j_i are those found in this study, sr is assumed to be 0.5. When transients are considered, S^j_i is the value from models assuming no transient effects i.e. a weighted value between the transients and the non-transients animals. Individuals of both species start to reproduce at the age of 3 (Oro et al. 2004).

The vector V_i+1 could be written as:

(Note that the pre-breeding survival was assumed constant and age-independent). The dominant eigen value of matrix A^j_i is the population growth rate between time i and i+1 (see also (Case 2000, Caswell 2001). A possible measure of synchrony is the cross-correlation between population growth rates. If the parameters found would give synchronous dynamics between the two colonies of each species, we expect a significant correlation between their respective population growth rates. Note that for the sake of simplicity the model does not consider the presence of transients in neither species, and it should be considered a conservative test of between-colony synchrony. We assumed that populations started with one individual per age class.

LITERATURE CITED

Burnham, K. P., D. R. Anderson, G. C. White, C. Brownie, and K. H. Pollock. 1987. Design and Analysis Methods for Fish Survival Experiments Based on Release Recapture. American Fisheries Society, Bethesda, Maryland, USA.

Case, T. J. 2000. An illustrated guide to theoretical ecology. Oxford University Press, Oxford, UK.

Caswell, H. 2001. Matrix Population Models (second edition). Sinauer Press, Sunderland, Massachusetts, USA.

Choquet, R., A.-M. Reboulet, J.-D. Lebreton, O. Gimenez, and R. Pradel. 2005. U_Care2.2 : User's Manual http://ftp.cefe.cnrs.fr/biom/Soft-CR/. CEFE-CNRS, Montpellier.

Oro, D., E. Cam, R. Pradel, and A. Martínez-Abraín. 2004. Influence of food availability on demography and local population dynamics in a long-lived seabird. . Proceedings of the Royal Society London, Series B 271:387–396.

Pollock, K. H., J. D. Nichols, C. Brownie, and J. Hines. 1990. Statistical inference for capture-recapture experiments. Wildlife monographs 107.