Ecological Archives A024-074-A1

J. Timothy Wootton, Douglas A. Bell. 2014. Assessing predictions of population viability analysis: Peregrine Falcon populations in California. Ecological Applications 24:1251–1257. http://dx.doi.org/10.1890/13-1323.1

Appendix A. Description of structure and parameterization methods of model presented in Wootton and Bell (1992).

The model was structured as a two-stage (non-breeders and adult breeders) matrix model with two metapopulations and a vector describing population supplementation by captive-reared birds:

EqA1     (A.1)

where Fx,t is the number of non-breeding birds in subpopulation x (n-north, s-south) at time t, Nx,t is the number of breeding adults in subpopulation x at time t, bx is the annual fledging rate per breeding bird in subpopulation x, yx is the survival rate of non-breeding birds in subpopulation x, rx is the rate of survival and recruitment to the breeding population of non-breeding birds in subpopulation x, sx is the survival rate of breeding birds, m is the probability that a non-breeding bird moves to a different subpopulation in a year, c is the probability of surviving movement among subpopulations, f is the proportion of reared birds released in the northern subpopulation, and I is the total number of reared birds released. The dashed lines in the matrix of vital rates of free-living birds illustrate how the matrix is subdivided to account for spatial structure: 2 × 2 sub-matrices along the diagonal are the portions of the model describing vital rates of birds that stay within a subpopulation, and off-diagonal sub-matrices describe the fate of birds that move between subpopulations. Note that the variables and birth parameters used here include both males and females to match the population census data used in the paper, rather than the common practice of modeling just females as did Wootton and Bell (1992). To project the population when introductions were terminated, we set I = 0, which effectively eliminates the vector on the right-hand side of the equation.

The basic model has density-independent vital rates. To introduce density dependence, we placed a hard cap on the number of breeding birds in a subpopulation, reflecting density dependence arising from a limited number of breeding territories (Tx). We allowed birds that did not find territories to remain in the population as non-breeding floaters. Hence, when the maximum cap in the northern subpopulation was reached, for example, in the absence of population supplementation the model changes to:

EqA2     (A.2)

where dn is the survival rate of floaters.

Details of our methods and data sources for estimating parameters are in Wootton and Bell (1992). Fledging success (bx) and numbers of birds introduced (Ix) were estimated from detailed annual nest monitoring data and captive rearing records taken between 1980 and 1992 by the Santa Cruz Predatory Bird Research Group in California. Yearling survival (yx) was taken from studies of peregrine falcons in the United Kingdom, and movement among subpopulations (m) was estimated from data on distance between the point of release of introduced female birds and their documented nesting territories for populations in the midwestern United States. Recruitment rate to the breeding population (rx) was estimated using data on rates of recruitment of marked, captive-reared birds to the breeding population in California, and then factoring out the estimated yearling survival. Maximum numbers of territories (Tx) were derived from historical records from California. Effects of movement on survival were assumed to be non-existent (c = 1) and survival of floaters (dx) was assumed identical to breeding adults (sx). Adult breeder survival was derived by rearranging the model to solve for sn and ss, using annual data for population size, fledging success and numbers of introduced birds, and estimates for all other parameters, and then averaging the results across years.

 

Literature cited

Wootton, J. T., and D. A. Bell. 1992. A metapopulation model of the peregrine falcon in California: viability and management strategies. Ecological Applications 2:307–321.


[Back to A024-074]