*Ecological Archives* E093-230-A1

Guillaume Péron, David N. Koons. 2012. Integrated modeling of communities: parasitism, competition, and demographic synchrony in sympatric ducks. *Ecology* 93:2456–2464. http://dx.doi.org/10.1890/11-1881.1

Appendix A. Matrix model used in the state-space formulation, full parameterization of the variance–covariance matrix between model parameters, and regression between the population counts time series.

**1) Matrix model used to estimate species-, age- and sex-specific demographic parameters in the state-space model**

F, S, and τ respectively denote annual fecundity (number of offspring that reach the age at which they can be fitted with a band, per female that is present on the breeding grounds in May), annual survival (from 1 Oct. to 1 Oct.) and average first-year breeding probability. Subscripts R and C stood for the species (redhead/canvasback), HY and AHY for the age class (first year/after first year; see text), and f and m for the sex (female/male). Subscripts for time variation are omitted for clarity. Because survival was estimated from October to October, but population size was surveyed in May, the HY survival in the above equation corresponded to the 7-month period from October to May. We moreover assumed a 50:50 sex ratio at birth.

__2) Parameterization of the Σ variance-covariance matrix__

__3) Raw data and regression between redhead and canvasback counts for the mid-continent populations, 1960–2010__

FIG. A1. Left panel: Raw count data. Right panel: Result of the linear regression and correlation between counts of redhead and canvasback abundance, standardized to a mean of 0 and a standard deviation of 1; colors indicate pond number P, standardized to a mean of 0 and a standard deviation of 1.