This latest attack on animal research involves the claim that our bodies are just too complex. The claim goes that in response to any intervention or manipulation, any small changes in the initial conditions will lead to very large difference in results, a property that is characteristic of so-called chaotic systems.
However, complex and chaotic systems can in fact be analyzed and their behavior can be predicted on appropriate time scales. Consider the prediction of weather. Weather is in general chaotic but it is predictable on a time-scale of about a week. Many sophisticated learning algorithms (see references below) have been proposed that allow the prediction of chaotic time series by learning the nonlinear dynamics from observations. Thus, chaotic behavior does not necessarily imply unpredictability at all time scales.
In my field of research we investigate the workings of the brain; certainly a complex system. Lets do a simple experiment. Put your right hand on top of your right knee. Now, touch your nose with your index finger. Lets try again. Hand down; touch your nose. Once more: hand down, touch your nose. Not too difficult, right? However, every single time you initiated the movement the neurons in your brain were in a somewhat different state. If your brain was chaotic on these short time scales then every time you would reach for your nose you would miss because the initial condition for each execution of the movement was slightly different -- sometimes you would land on your forehead, sometimes on your mouth, and sometimes on your eye. I assume this did not happen to you.
If the brain was a truly chaotic system you would not be able to plan your day, to get up and brush your teeth, have your breakfast and head to work. You would not be able to retrieve a mental map of the city and drive yourself around. You would not be able to do any of these things.
If human physiology were to be described by highly chaotic dynamics on the timescales that drugs act on your body then there would be no warranty that the same drug may work on the same person every single time. If that were true, not only animal research would be impossible but human research as well.
Fortunately, the claim is false... and here is the weather forecast for tomorrow (despite long term chaotic behavior) coming to you as a courtesy of nonlinear prediction techniques.
For the mathematically inclined, here is some literature on the prediction of chaotic time series: