10.1. Determining yield in response to specific colony density

The reader is directed to sections 4 and 5 that explain these methods in detail, bearing in mind that for our immediate purpose we are interested in the change in net income given a particular increase in hive number. Considering that increased pollinator abundance should augment yield at a decelerating rate to the point that additional individuals do not further increase (e.g. pollen saturation) (Fig. 19) or even decrease (e.g. pollen excess) yield (Chacoff et al., 2008; Morris et al., 2010; Garibaldi et al., 2011), valuation analysis should include a range of hive densities (i.e. from zero to high numbers). At the very least two situations are needed for comparison: fields with hives vs. fields without hives (control). Each treatment should be replicated with several fields (Prosser, 2010), and the number of necessary fields can be estimated using standard statistical techniques (Anderson et al., 2008). In brief, more fields are necessary if we desire higher statistical power or if we face highly heterogeneous conditions within and between fields. Pollination provided by wild insects should be also measured, as the effect of adding hives of honey bees on crop yield will greatly depend on the "base" level of pollination being provided by wild insects. In addition, the presence of wild insects can enhance honey bees pollination behaviour (Greenleaf and Kremen, 2006; Carvalheiro et al., 2011).

Fig. 19. The marginal benefit to crop yield (e.g. tonnes per ha) of each additional bee colony decreases with colony number. When this marginal benefit equals the cost generated by more yield (variable cost) plus the cost of renting a hive, the net income generated by the addition of the hive is zero and is no longer economically beneficial for the farmer.

1297PN revised Fig 19