Fractional Cell Kill Hypothesis

Suppose you had a field of crops and there are insects on the field, eating away at your harvest, so you want to apply a pesticide to get rid of the insects.  Suppose the agricultural extension service guy told you how much of the chemical to apply (gallons of pesticide per acre of field) and how to configure the spray tanks and nozzles.  Following this protocol of pesticide application, you find 90 percent of insects are killed.  By trying this method over time and in different fields, you find this 90 percent is constant, no matter how many insects are on the land.  If there are twice as many insects, you still kill 90 percent. If there are half as many insects, you still kill 90 percent. The relationship between percent eliminated and number of insects is therefore said to be scale invariant.  It follows a logarithmic pattern.

Now, you could change the regimen of your pesticide application – say by increasing gallons per acre of application or a different spraying technique, and that might change your kill rate to 95 percent or 97 percent or 80 percent.  But that’s a separate issue. Within your given technology/operating procedure the kill rate is fixed. The number of pests killed varies with the number of pests on the field, but the percentage of pests killed is the same.

Do actual agriculture operations work that way?  That is not clear, but chemotherapy treatment of tumors does follow this pattern.  Study after study has found this logarithmic relationship – it doesn’t matter how many cells a tumor has, a given chemo regimen destroys a certain fraction of them.