## Interactions

Since the environment contains numerous toxins, we are interested in their combined effect. We worry that two pesticides taken up by the same organism may have a much greater effect than either one alone. To detect such an effect, we must first define the situation expected when two toxins act independently.

First, we need to establish the following fact: If d is the dosage of toxin A producing a given response, 1/d is a direct measure of the toxicity of A. By direct measure we mean a quantity that is proportional to toxicity. For example, the LD50 is the dosage that results in 50% mortality. However, LD50 is inversely related to toxicity. We would consider a toxin that is twice as toxic as A to have half the LD50 , and one 10 times as toxic to have one-tenth the LD50. Thus, 1/LD50 is a satisfactory measure of toxicity.

Next, let us define a parameter to describe the mixed dosage of two toxins, A and B, with LD50 A and LD50B, respectively. The mixed dosage, dt, will simply be the sum of the individual dosages, dA and dB, respectively. Then the fraction of the total dosage, 1A, will be