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 Change-in-ratio (CIR) methods can provide an effective, low cost approach for estimating the size of wildlife populations. They rely on being able to observe changes in proportions of population subclasses that result from the removal of a known number of individuals from the population. These methods were first introduced in the 1940's to estimate the size of populations with 2 subclasses under the assumption of equal subclass encounter probabilities. Over the next 40 years, closed population CIR models were developed to consider additional subclasses and use additional sampling periods. Models with assumptions about how encounter probabilities vary over time rather than between subclasses also received some attention. Recently, all of these CIR models have been shown to be special cases of a more general model (Udevitz and Pollock 1991, 1992, 1995). Under the general model, information from additional samples can be used to test assumptions about the encounter probabilities and to provide estimates of subclass sizes under relaxations of these assumptions. These developments have greatly extended the applicability of the methods. CIR methods are attractive because they do not require the marking of individuals, and subclass proportions often can be estimated with relatively simple sampling procedures. However, CIR methods require a carefully monitored removal of individuals from the population, and the estimates will be of poor quality unless the removals induce substantial changes in subclass proportions.
Some CIR estimators have explicit forms, but others have to be found numerically. We have used SAS PROC NLIN (SAS 1989) to implement an iteratively weighted least squares approach for obtaining CIR estimators in cases where numerical procedures were required. Click on the link below for examples of the SAS code. Details of this approach are given by Udevitz and Pollock (1991, 1995).
SAS Institute Inc. 1989. SAS/STAT user's guide, version 6, fourth edition, volume 2. SAS Institute, Inc., Cary, North Carolina, USA.
Udevitz, M. S., and K. H. Pollock. 1991. Change-in-ratio estimators for populations with more than two subclasses. Biometrics 47:1531-1546.
Udevitz, M. S., and K. H. Pollock. 1992. Change-in-ratio methods for estimating population size. Pages 90-101 in D. R. McCullough and R. H. Barrett, eds. Wildlife 2001: populations. Elsevier Applied Science, New York, NY, USA.
Udevitz, M. S., and K. H. Pollock. 1995. Using effort information with change-in-ratio data for population estimation. Biometrics 51:471-481. |
