# 4.3.3.5. Non-detection and non-sampling errors

Two kinds of errors affect estimated number of drone-producing queens:

1. Non-detection errors (the probability of obtaining two identical genotypes in two different individuals by chance). Non-detection errors (NDE) are determined by the number of markers employed and their level of polymorphism and are an indicator of the resolution of these markers. It should always be reported along with the results, but there is no need to correct the results. To calculate NDE the following formula can be used:

where

*q _{i}* are the
allele/haplotype frequencies at the first locus,

*r*are the allele/haplotype frequencies at the second locus, and

_{i}z

*are the allele/haplotype frequencies at the last locus.*

_{i}This calculation assumes all loci/linkage groups are unlinked and under Hardy-Weinberg equilibrium.

2. Non-sampling errors (the number of queens remaining undetected because of an insufficient sample). In contrast to NDE, the final number of queens detected should be corrected for non-sampling errors (NSE). In other words, the number of undetected queens should be accounted for. The following procedure describes how to account for NSE.

2.1. Construct a frequency distribution table with the number of drones found to be assigned to each colony (see Fig. 27).

2.2. Fit a Poisson distribution to the real
data by calculating the expected frequency for each category

(i.e. each
colony).

Expected frequencies of a Poisson
distribution can be calculated using most commercial statistical packages

(e.g.
STATISTICA or SPSS).

2.3. Obtain the expected frequency for the zero or less than one category.

2.4. Adding the undetected colonies (or
colonies with an expected frequency of zero, see Fig. 27) to the detected

ones
to correct result for non-sampling errors.

*Fig. 27.*** **Estimating the
number of non-sampled colonies through a fitted Poisson distribution.** **While observed frequencies are plotted
with blue bars, expected frequencies (fitted Poisson distribution) are shown in
a red dashed line. In this example, the number of non-detected colonies is 4.7.