4. A worked example
Although a single recommended experimental design, including sample size, may be difficult to find consensus on given the factors mentioned above, we provide below a recommendation for experimental design when using groups of caged honey bees to understand the impact of a certain factor (e.g. parasite or pesticide) on honey bees. For our example, imagine the focus is the impact of the gut parasite Nosema ceranae and black queen cell virus on honey bees. One should consider the following:
- Each cage should contain the same number of honey bees, and be exposed to the same environmental conditions (e.g., temperature, humidity, feeding regime, see the BEEBOOK paper on maintaining adult workers in cages, Williams et al., 2013). Each cage of treated honey bees is a single experimental unit, or unit of replication. Since there is no other restriction on randomisation, other than the systematic sampling from different colonies for each replicate (see below), this is a completely randomised design. If one instead put only bees from one colony in a cage, but made sure that all treatments were evenly represented for each colony (e.g. 5 cages from colony A get treatment 1, 5 cages from colony A get treatment 2, etc.), then we would have a randomised complete block design.
- We recommend 4-9 replicate cages per treatment. Honey bees should be drawn from 6-9 different colonies to constitute each replicate and equal numbers of honey bees from each source colony should be placed in each cage (i.e., in all cages, including controls and treatments) to eliminate effects of colony; this makes only cage a random factor. For example, if one draws honey bees from 6 source colonies and wants cages to contain 24 honey bees each, then one must randomly select 4 honey bees from each colony for each cage. If one wants to keep colony and cage both as random effects (e.g. to estimate effects of a pathogen on bees from a population of colonies, only some of which were sampled), one should not mix bees from different colonies in the cages. Note that the minimum number of bees also depends on the experimental design. Darchen (1956, 1957) showed that comb construction only started with a minimum number of 51-75 workers and a queen; in cases of a dead queen, 201-300 workers were needed (summarised in Table 14.1 in Hepburn, 1986). Furthermore, cage design itself can influence behaviour (Köhler et al., 2013) therefore identical cages should be used for all replicates. A group size of 15 workers ensures that the impact of experimentally administered Nosema and black queen cell virus in honey bees in general is measured, as opposed to impacts of these parasites on a specific honey bee colony. It also ensures that chance stochastic events, such as all the honey bees dying in a specific treatment cage, do not unduly affect the analysis and interpretation of results. Low numbers of source colonies (i.e. low numbers of replicates) could lead to an over- or under-estimation of the impact of the studied factor(s). A computer simulation based on Monte-Carlo methods (see section 3.2.3.) and parametric statistics supports the appropriateness of the proposed values. Experiments across replicate colonies must be conducted at approximately the same time, because effects such as day length and seasonality can introduce additional sources of error (see section 2.1.1. and section 3. for relationships between model complexity and sources of error).