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Slide 3 of 17


With these two assumptions about bee and plant populations, there is clearly a tradeoff between bee yields and seed yields. Bee yields (purple line) reach a peak when a relatively small bee population is introduced into the field. As more bees are introduced, density dependent mortality causes the bee offspring population to decline. The black line through the middle of the graph indicates where the number of introduced bees equals the number of offspring. Where the purple female offspring curve crosses the black line, the introduced bee population results in a sustainable yield of offspring bees. In this graph, the sustainable yield of bees is less than the maximum bee yield, and seed yield (red line) is still increasing if more bees are introduced into the field. Seed yields are maximized when a relatively large number of bees are introduced into the field. In summary, if there is density dependent bee mortality, then the optimum introduced bee population for maximizing bee reproduction is lower than the optimum bee population for maximizing seed yields.

Download a free demo copy of isee Player  from isee Systems. You need this software on your computer to run the program.

 Right mouse click the hyperlink below  and select "save target as..." :
     With density dependent bee mortality
     Without density dependent bee mortality

The figure above, and the figure on slide 4 were made by running the model multiple times, each time increasing the number of introduced bees.  Results at the end of the run were copied from the table in the model to an excel file.  Download the excel file.

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