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Problem ER15

The golden-beak parrots (Parrotus chrysaetos) were captured in the past for ornamental purpose; in recent times they have been protected in the Montes Rojos reserve. Here below you can find the population numbers as recorded by the Guanavaca Ornithological Institute

Year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Numbers 21 98 285 379 273 313 290 345 330 288 301 314

Fit a Ricker model to the population data (Hint: calculate the finite growth rates, then take logarithms and find the appropriate regression line). Find the nontrivial equilibrium of the deterministic model and assess its stability. Which is the long-term average of the parrot population at Montes Rojos?