## 4 Discussion  
The start date of 1 August for the temperature accumulations and the modeling component of the study was chosen based on information in the scientific literature regarding wheat harvest times in Slovenia. In a previous experiment describing effects of _Oulema melanopus_ (L.), the cereal leaf beetle, on field wheat, the wheat was planted on site at the University of Ljubljana, Slovenia, in Autumn and harvested on 19 and 25 July [22]. In a different experiment in which wheat was grown in Serbia, which is in the Balkan peninsula near Slovenia, the harvest date was also late July [23]. Thus, the start date of August 1 for the simulations was chosen to correspond to an average binning date for wheat harvested in Slovenia, regardless of location. The 10 locations for weather data were chosen to give a geographic representation of historical weather data in Slovenia. Most of the published papers on _Sitophilus_ spp. in stored products in Slovenia focus on _Sitophilus zeamais_ (Motchulsky), the maize weevil [24]. However, the temperature requirements  
Figure 4: Predicted average bin temperatures in unaerated and aerated wheat stored in Lesce, Slovenia from 1 August to 30 November (**A**); and predicted numbers of eggs, larvae, and adults of _Sitophilus oryzae_ in unaerated wheat (**B**). Predicted numbers of each life stage on November 30 in aerated wheat are listed as text (**B**). In the X-axes, date is given in Month-Day format. and population development of this species on wheat is similar to those for _S. oryzae_, which is a primary pest of wheat in the United States (US) [25]. _Sitophilus zeannais_ is usually associated with corn (maize) in the US [25]; however, this species can readily feed on wheat as well. Thus, the predicted population development for _S. oryzae_ generated by the TAMU-Beaumont model should be applicable to other _Sitophilus_ species. The first aeration methodology used a cyclical aeration approach, based on the theoretical assumption that 120 h below a given temperature threshold are needed to cool wheat to that level, using an airflow rate of 0.12 m\({}^{3}\)/min/MT. This calculation is independent of the size of the storage bin and assumes the aeration fan motor is powerful enough to deliver the specified airflow rate through the wheat mass. This approach was used to stratify Slovenia into different aeration zones to predict feasibility of using aeration as part of pest management programs, similar to what has been done for different regions of the US [9; 10; 11; 12; 13]. However, this hourly time estimate is a theoretical estimate, and in actual practice more hours may be required to cool the bin. Studies conducted by [PERSON] and [PERSON] [8; 26], in which wheat stored in Kansas was initially cooled to 24 \({}^{\circ}\)C during in the summer months, showed that more than 200 h below this 24 \({}^{\circ}\)C threshold were required for this initial cooling. The cooling cycles to 15 \({}^{\circ}\)C in autumn required between 120 and 150 h.  
The degree day approach described in this study, which has been used to predict generation times for crop pests [15], was used to determine if a generation of _S. oryzae_ could be produced in the absence of aeration, starting on 1 August. A degree-day methodology was previously used to predict generation times for _S. oryzae_ on bagged rice stored in Japan [27], but the degree-day approach outlined in this manuscript was the first time it was used to predict generation times for a stored product insect. The advantage of a degree-day approach is that it is simple to use, easy to understand, and valid for comparison purposes. A degree-day approach also fits with aeration models, because most aeration models for stored grains assume that the peripheral regions of a grain mass will cool much more slowly than the bulk mass, and temperatures on the surface of the grain mass may approximate ambient temperatures [28; 29; 30].