Ecological Archives M078-006-A2

Steven R. Beissinger, Joseph M. Wunderle, Jr., J. Michael Meyers, Bernt-Erik Sæther, and Steinar Engen. 2008. Anatomy of a bottleneck: diagnosing factors limiting population growth in the Puerto Rican Parrot. Ecological Monographs 78:185–203.

Appendix B. Parameterization of the stage-based deterministic matrix model.

The stage-structured, prebreeding deterministic population model for the Puerto Rican Parrot (Fig. B) used an annual time step. A year started in February with a census followed by nesting in March, fledging in July, a period of mortality, aging and census the following year. Nodes are 1-year-olds, nonbreeders (NB), and breeding pairs (BP).

Estimating Survival and Transition to Breeding

P0 is survival of juveniles from fledging in July to census in the following February (seven months). Snyder et al. (1987) resighted 75% of 32 fledged young the following year at the onset of nesting with their parents. Based on data in Lindsay et al. (1994) for 15 radioed juveniles, Collazo et al. (2000) derived an annual estimate of survival of 32.5%, which results in 91.1% monthly survival or a 52% survival to census (seven months). We used the mean of the two values weighted by the number of birds studied, which yielded 68%.

Survival of breeders (P3) was estimated as 0.88 from pair turnover rates (Fig. 6, Table 3).

G is the rate of ascendancy of nonbreeders to breeder status, which we estimated by dividing the number of new breeders (b*) each year by the number of nonbreeders in the previous year. To get the latter value, we used annual count data (Fig. 1) and subtracted the number of breeders (bt-1) from the total (Nt-1) and then subtracted an estimate of the number of one-year olds or young produced the previous year (ft-1) that survived to year t assuming a survival rate of Po:

The 26-yr mean was G = 0.12 + 0.13 (SD).

In the absence of data to the contrary, annual survival of nonbreeders was set equal to P3 since nonbreeders would be 2+ years old. Nonbreeders might be expected to survive better than breeders because they are not subjected to the risks or costs of reproduction, although the only data available for parrots suggests nonbreeders have lower survival (Sandercock et al. 2000). Since annual survival of nonbreeders is equal to P2 + G, it follows that P2 = P3G.

P1 could be set equal to adult survival because most mortality occurs in the first months after fledging (Lindsey et al. 1994). On the other hand, Snyder et al. (1987) suggested that the mortality rate of nonbreeders from 1973–1979 was twice as high (15%) as breeders (8%) based on annual count data, but this estimate greatly overestimates mortality of one-year-olds because changes in count data included mortality of juveniles. If one-year-olds did have twice the morality rate of adults, then P1 = 0.76. In the absence of data, we set P1 = 0.8 or 10% less than poorer survival of adults and nonbreeders.

Estimating Fecundity

We estimated annual fecundity (m) as the number of female offspring produced per breeding female from the following:

m = s*y + r*(1-s)*s*y

where s is percentage of nests that are successful or fledge at least one young, y is number of female young produced per successful nest, and r = probability of renesting within a breeding season if a nest fails. Values of s and y vary by analysis and are presented in the manuscript. We calculated r as the likelihood of renesting after failure by pairs from 1990–2000. Renesting was documented in 3 of 16 nests (18.75%) that failed during this period from natural causes. Using these values and assuming a 50:50 sex ratio of offspring, m = 0.82

   FIG. B1. Life cycle diagram and prebreeding projection matrix for the Puerto Rican Parrot based on breeding pairs (BP), nonbreeders (NB) exceeding 1 year of age, and one-year-olds (1). Demographic parameters are: (1) m3 is the number of female offspring produced by a breeding pair; (2) P0 is the survival from fledging to census the following year; (3) P1 represents annual survival of nonbreeders that remain as nonbreeders; (4) G is the annual survival and transition of nonbreeders to become breeders; and (5) P3 is the survival of breeders. The projection matrix A is shown.


[Back to M078-006]