A Capture–Recapture Model to Estimate the Size of Criminal Populations and the Risks of Detection in a Marijuana Cultivation Industry


Originally developed in biology, capture-recapture methodologies have increasingly been integrated into the study of human populations to provide estimates of the size of “hidden populations.” This paper explores the validity of one capture-recapture model—Zelterman’s (1988) truncated Poisson estimator—used to estimate the size of the marijuana cultivation industry in Quebec, Canada. The capture–recapture analysis draws on arrest data to estimate the number of marijuana growers “at risk of being arrested” for a period of five years (1998–2002). Estimates are provided for growers involved in two different techniques: (1) soil-based growing, and (2) hydroponics. In addition, the study develops an original method to estimate the prevalence of cultivation sites “at risk of detection.” A first set of findings shows that the cultivation industry is substantial; the estimated prevalence of growers compares to estimates of marijuana dealers in the province. Capture–recapture estimates are also used to compare the risks of being arrested for different types of offenders. Results indicate that hydroponic growers—those involved in large scale and sophisticated sites—face lower enforcement-related risks than growers involved in smaller enterprises. The significance of these findings is discussed in the context of the widespread development, both in Europe and in North America, of a successful domestic production-driven, rather than importation-driven, marijuana trade.

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  1. 1.

    The SPVM is assumed to intervene on a similar number of indoor and hydroponic cases than the rest of the province. For example, a newspaper article reported that the SPVM discovered 28 hydroponic greenhouses in 1998 (Breton 2000), whereas our QPP data indicate that they discovered 31 sites for that same year. This underestimate of indoor and hydroponic seizures will be taken into account when analyzing the risks of detection later in the paper.

  2. 2.

    Using data on seizures may not reflect the distribution of sizes for the industry as a whole but only those at risk of being detected, a convenient bias for an analysis concerned with providing estimates for this type of sample.

  3. 3.

    The very low proportion of non commercial sites found in the sample is interesting. Qualitative studies like those of Weisheit (1992), or Hough et al. (2003) almost exclusively interviewed small-time growers which gave the impression that they represented the majority of growers. Conversely, by relying on police data, the current study probably overemphasizes larger cases, but nonetheless demonstrates that they are far from scant, at least in the region under study.

  4. 4.

    It is likely that these figures on the number of plants per cultivation site are inflated, because police typically treat all types of plants equally: plants of low quality, or baby plants, are counted even though only a variable amount of these will reach maturity. The inflation rate is unknown, but is not a major problem for the purpose of this study as it is likely to be constant for all types of cultivation sites. However, the inflated figures would be problematic for a different study that wanted to estimate the quantity of marijuana produced in the province. Such an estimate would also be inflated.

  5. 5.

    The median is used because the distribution of sizes is highly skewed. The mean number of plants seized is 128, 372, and 816 plants for outdoor, indoor, and hydroponic sites, respectively.

  6. 6.

    One respondent was referred by a colleague criminologist who was supervising him while he served the end of a federal sentence in a halfway house in Montreal after being found guilty of cannabis cultivation. Two other respondents were referred by a criminology student after a seminar I taught on cannabis cultivation. The six others were referred to me by mutual acquaintances after learning about the research.

  7. 7.

    The theoretical distributions can easily be estimated by creating a spreadsheet similar to the Poisson distribution calculator available on Carnegie Mellon University Department of Biology’s website: www.bio.cmu.edu/courses/03438/PBC97Poisson/PoissonCalc.xl. The arrest rate parameter necessary for such calculation must first be estimated by Eq. 1, i.e. by dividing the total number of arrests by Z, the estimated prevalence of growers.

  8. 8.

    The survey also included the cities of San Francisco and Bremen, Germany, but findings were either unclear, or the amount of users interviewed insufficient to reach any conclusions. For example, only one user out of 262 in San Francisco reported growing marijuana at the time of interview, but more than 79 said they had done so in their lifetime. In Bremen, 4% of respondents said they grew marijuana at the time of the interview, but the sample is simply too small (N = 50) to make any inference about the prevalence of growing among users in this city.

  9. 9.

    Note that the risks for soil-based growers remain higher overall, even when the adjustment procedure is taken into account (Table 4, Appendix A).

  10. 10.

    Because very few outdoor soil-based growers are likely to be at risk given the low percentage of outdoor seizure that lead to an arrest (14%), the figures presented for soil-based cultivation mostly concern indoor growers.

  11. 11.

    I used a simple linear regression model of the form C = a + b*p, where C is the number of co-offenders per site and p is the number of plants grown per site. The regression coeffients are presented as following: for outdoor sites (n = 10): C = 2.805 + 0.0116*p; for indoor sites (n = 13): C = 2.955 + 0.0082*p; for hydroponic sites (n = 11): C = 2.981 + 0.0057*p.

  12. 12.

    The finding holds even when increasing the number of seizure cases by a factor of two––to compensate for the absence of most cases from Montreal.

  13. 13.

    One rather extreme scenario is to assume economies of scale for outdoor sites instead of hydroponic sites. For example, increasing the number of offenders necessary to produce 485 hydroponic plants from 5.8 to 7.8 produces an increase in risks from 3% to 4%, whereas a similar inverse operation for outdoor sites (reducing crew size from 5.5 to 3.5 co-offenders) decreases the risks of detection from 37% to 23%. In the end, the difference in risks between large outdoor and hydroponic sites (23% vs. 4%) remains very important.

  14. 14.

    Hydroponically produced marijuana is typically stronger in the drug’s psychoactive content (Tetrahydrocannabinol, or THC) than soil-produced herb. Interviewed growers report that it is also sold at higher prices, and hydroponic growers can cultivate more crops per year than with any other method.


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I would like to thank Pierre Tremblay for his decisive comments on an earlier version of this paper. Peter Reuter, Therese Brown, Carlo Morselli, Maurice Cusson, Mathieu Charest, Julien Piednoir, Sue-Ming Yang and three anonymous reviewers also provided useful suggestions. Finally, I am grateful for the contributions of Marteen Cruijff, Paul Fugère, Chloé Leclerc, Maïa Leduc, and Barbara Wegrzycka in analyzing some of the data presented in the paper.

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Correspondence to Martin Bouchard.

Appendix A

Appendix A

Adjusting the population estimates

An important difference between the seizure and the arrest data set is that the latter does not distinguish between outdoor and indoor soil-based growers. The distinction is important, especially for assessing the differential risks of detection. The procedure starts by establishing the proportion of soil-based growers involved in outdoor and indoor settings. Seizure data for 2000–2001 show that 68% of soil-based seizures are made on outdoor sites (2,075 total cases out of 3,051). Because 13.9% of outdoor seizures lead to arrest, it is estimated that 288 outdoor growers were arrested in 2000–2001 (assuming one arrested offender per case). A similar calculation for indoor growers gives 742 offenders, for a total of 1,030 soil-based growers arrested, 28% of which (288) are estimated to be outdoor growers. Because the number of offenders arrested per case does not vary by type of method or location (1.3 offenders per case), it is expected that 28% of the annual population of soil-based growers will be involved in outdoor production, and the remaining 72% are indoor growers.

A second adjustment was incorporated into the figures presented in Table 6. Capture-recapture estimates are valid models to estimate populations at risks of being arrested; these models are not designed to capture segments of a population that are shielded from arrest, if they exist. Although mathematically, every active offender has at least a small probability of being arrested (Greene and Stollmack 1981), data on seizures reveal that the majority of outdoor cultivation cases never lead to an arrest. In 2000–2001, 13.9% of outdoor seizures led to an arrest, whereas 76.3% of indoor (soil-based) and 95% of hydroponic seizure cases led to at least one arrest. Thus, prevalence estimates were adjusted to reflect the percentage of offenders affected by a seizure but never arrested, by type of technique (an inflation rate of 86.1% (or 100–13.9%) for outdoor cases, 24% for indoor ones). This adjustment is unnecessary for hydroponic growers, because almost all seizures involve at least one offender arrested. This second adjustment increased the prevalence of soil-based growers by an average of 10,000 growers per year.

Table 6 Adjusted populations of indoor and outdoor soil-based growers, 1998–2002

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Bouchard, M. A Capture–Recapture Model to Estimate the Size of Criminal Populations and the Risks of Detection in a Marijuana Cultivation Industry. J Quant Criminol 23, 221–241 (2007). https://doi.org/10.1007/s10940-007-9027-1

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  • Marijuana cultivation
  • Risks of arrest
  • Risks of detection
  • Size of criminal populations
  • Capture–recapture methodologies