Ouabache

There are 14 bottles of wine and one is tainted such that,
a single sip of the tainted bottle is lethal. It takes up to 24 hours for full effect of the toxicity.
If you have only 4 lab animals to test all 14 bottles of wine;
what experimental design might you use, to determine which bottle was lethal?
You need to determine the answer after 24 hours.

For those who heard this question on a popular radio program, (or have heard this question before) please let some of the others give this a try. I am curious of your approach, if you come from a biology academic background, versus those with a cross-disciplinary education.

(hint: some maths may be used)