Stratified-Petersen Analysis System

The Stratified-Petersen Analysis System (SPAS) is designed to estimate abundance in two-sample capture-recapture experiments where the capture and recaptures are stratified. This is a generalization of the simple Lincoln-Petersen estimator. Strata may be defined in time or in space or both, and the s strata in which marking takes place may differ from the t strata in which recoveries take place. When s=t, SPAS reduces to the method described by Darroch (1961) <>. When s>. Schwarz and Taylor (1998) describe the use of SPAS in estimating return of salmon stratified by time and geography. A related package, BTSPAS, deals with temporal stratification where a spline is used to model the distribution of the population over time as it passes the second capture location. This is the R-version of the (now obsolete) standalone Windows program available at <>.

Stratified Petersen Analysis System in R

Versions and installation

  • CRAN Download the SPAS package

  • Github To install the latest development version from Github, install the newest version of the devtools package; then run

devtools::install_github("cschwarz-stat-sfu-ca/SPAS", dependencies = TRUE,
                        build_vignettes = TRUE)


This is an R version of the Windoze program SPAS to estimate population abundance using a Stratified Petersen Estimator (Darroch 1961; Plante et al 1998; Schwarz and Taylor, 1998)

The user is allows to pool rows and/or columns prior to analysis but the number of rows must be less than or equal to the number of columns (s <= t). The conditional likelihood formulation of Plante et al (1998) is used to estimate the parameters.

Because the data are physically pooled prior to analysis, it is not yet possible to compare different poolings to see which is most appropriate - this is under active investigation. A good discussion of how to decide on pooling rows/columns is found in Schwarz and Taylor (1998).


Darroch, J. N. (1961). The two-sample capture-recapture census when tagging and sampling are stratified. Biometrika, 48, 241–260.

Plante, N., L.-P Rivest, and G. Tremblay. (1988). Stratified Capture-Recapture Estimation of the Size of a Closed Population. Biometrics 54, 47-60.

Schwarz, C. J., & Taylor, C. G. (1998). The use of the stratified-Petersen estimator in fisheries management with an illustration of estimating the number of pink salmon (Oncorhynchus gorbuscha) that return to spawn in the Fraser River. Canadian Journal of Fisheries and Aquatic Sciences, 55, 281–296.


SPAS 2018.11.22

  • First release of conversion of Windoze SPAS to R SPAS

Reference manual

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2020.1.1 by Carl James Schwarz, a year ago

Browse source code at

Authors: Carl James Schwarz

Documentation:   PDF Manual  

GPL (>= 2) license

Imports BB, MASS, Matrix, msm, numDeriv, plyr, TMB

Suggests knitr, rmarkdown

Linking to TMB, RcppEigen

See at CRAN