Mathematical programming models for determining the optimal location of beehives.

Farmers frequently decide where to locate the colonies of their domesticated eusocial bees, especially given the following mutually exclusive scenarios: (i) there are limited nectar and pollen sources within the vicinity of the apiary that cause competition among foragers; and (ii) there are fewer pollinators compared to the number of inflorescence that may lead to suboptimal pollination of crops. We hypothesize that optimally distributing the beehives in the apiary can help address the two scenarios stated above. In this paper, we develop quantitative models (specifically using linear programming) for addressing the two given scenarios. We formulate models involving the following factors: (i) fuzzy preference of the beekeeper; (ii) number of available colonies; (iii) unknown-but-bounded strength of colonies; (iv) probabilistic carrying capacity of the plant clusters; and (v) spatial orientation of the apiary.

Radiation inactivation of Paenibacillus larvae and sterilization of American Foul Brood (AFB) infected hives using Co-60 gamma rays.

The effectiveness of gamma radiation in inactivating the Philippine isolate of Paenibacillus larvae was investigated. Spores of P. larvae were irradiated at incremental doses (0.1, 0.2, 0.4, 0.8 and 1.6 kGy) of gamma radiation emitted by a 6°Co source. Surviving spores were counted and used to estimate the decimal reduction (D10) value. A dose of 0.2 kGy was sufficient to inactivate 90% of the total recoverable spores from an initial count of 105- 9 × 10³ spores per glass plate. The sterilizing effect of high doses of gamma radiation on the spores of P. larvae in infected hives was determined. In this study, a minimum dose (D(min)) of 15 kGy was tested. Beehives with sub-clinical infections of AFB were irradiated and examined for sterility. All the materials were found to be free of P. larvae indicating its susceptibility to γ-rays. After irradiation, there were no visible changes in the physical appearance of the hives' body, wax and frames. Thus, a dose of 15 kGy is effective enough for sterilization of AFB-infected materials.