How many soldiers are optimal for an aphid colony?

A number of aphid species produce sterile soldiers that defend their colony-mates against predators. How many soldiers should a colony produce? Assuming logistic growth of the aphid colony, we can theoretically deduce that soldiers will be produced until the marginal defensive efficacy of a soldier diminishes to rm/K, a ratio of two exogenous variables of the logistic equation, which are the maximum intrinsic rate of increase and carrying capacity. This conclusion holds true irrespective of the number of founders. As the number of founders increases, the entire colony size becomes larger, thus decreasing the percentage of soldiers. In case of multiple founders, each clone will produce the same number of reproductives that remain on the hostplant.