Craig Estimator

free program for population size estimation from mark-recapture data

What is Craig Estimator ?

Craig Estimator is freely available utility for population size estimation using mark-recapture data. It is based on the Craig's model (see Craig C.C. 1953: On the utilization of marked specimens in estimating populations of flying insects. Biometrika 40: 170-176). In Craig Estimator, the estimate is computed using bisection method.

Craig Estimator was created by Ondrej Sebek and Pavel Sebek.

How can I get it ?

Just download the file containing the program from Download page, unzip it, and run it on your computer. Currently, we provide two versions of the program:

- Craig Estimator 2.0 created in 2019 - written in Java, it requires Java to be installed on your computer. The program includes computation of 95% confidence limits of the population size estimation.

- Craig Estimator created in 2011 - written in C. It only computes population size and standard error of the estimate.

User interface

Craig Estimator is very easy to use. The program only asks you for number of captured individuals and number of captures. Then it computes the Craig's model and displays the results. Results are: estimate of the population size, standard error of the estimate, 95% confidence interval and lower and upper limits of the estimate (only available in version 2.0).

Interface of the original Craig Estimator

Craig's model in detail

Capture-recapture expriments (also called mark-recapture or capture-release-recapture experiments) are experiments, where an observer catches animals, marks them, and immediately releases them. Then he catches animals from the same population again, records marked individuals, and marks unmarked indiviuals. In his paper, C. C. Craig (1953) has formulated six methods for estimating population size of insects from capture-recapture data. Craig Estimator uses the first of these methods, Method 1 (hereafter referred as Craig’s model).


The model

According to the Craig’s model, population size n can be estimated from:

 log n - log (n - r) = s / n

where r is the number of captured individuals, and s is the overall number of captures (how many times these individuals were captured altogether).

The Newton-Raphson iterative method is often used to solve the equation. Craig Estimator uses the bisection method, which ensures that the root of the equation is always found. Standard deviation of the estimate, 95% confidence interval and lower and upper limits of the estimation are then computed (see Documentation for more information).



The Craig’s model has some assumptions about design of experiment the data come from. These are:

- individuals are marked and released back to the population,

- catchability is the same for all individuals (marked and unmarked),

- the population is stable during the sampling period,

- the model is originally designed for closed populations (individuals may not immigrate to or emigrate from the study population), however it can also be used for open populations if the sampling period is short and thus effects of immigration and emigration are negligible.


Craig’s model nowadays

More sophisticated and elaborate methods for population studies have been developed (Jolly-Seber model, Robust design, etc.), and the Craig’s model is no longer a method in the centre of researchers’ interest. However, it is often used for simple comparison with results of other methods. For instance, if assumptions of the models are not severely violated, the Craig’s model gives similar results to the Jolly-Seber model (its POPAN formulation). Although the Craig’s model was originally invented to estimate size of butterfly populations, it can be applied to all kinds of insects, or animals.


Craig’s model is quite simple. You only need the number of captured individuals and the number of captures to estimate the population size. You do not need to mark the individuals with specific tags to be able to distinguish them, and you do not need detailed encounter histories of all individuals.


Craig’s model only estimates the population size. In modern ecological studies, the population size is often of a minor importance, whereas parameters such as probability of survival or net growth population rate are fundamental for understanding the dynamics of populations in the course of time. Estimating these population parameters gives us a mean to predict a fate of a particular population in future. To be able to estimate these parameters, researcher has to switch to methods with greater demands on input data (complete encounter histories for each individual) but relevant to the problem of the study.

aUtHors of the program

Ondrej Sebek - Czech Institute of Informatics, Robotics, and Cybernetics, Czech Technical University in Prague, Czech Republic.

Pavel Sebek - Institute of Entomology, Biology Centre AS CR, Ceske Budejovice, Czech Republic.

If you have any question, advice, or if you encounter any problem with our program, feel free to contact us by sending an e-mail to: pav.sebek[at]