In a recent post, I mentioned the common confusion between randomness and stochasticity. A couple of commentors brought this issue up, so I’ll discuss it further (I really do read your comments…). Needless to say, with mathematicians and philosophers lurking around these ScienceBlogs, I’m giving one biologist’s amateur perspective on what these terms mean.
Let’s start with randomness. I don’t mean random in an existential ‘does life have any meaning?’ sense (Yawn. You bore me. Stop worrying about that and go do something meaningful. Or have an ice cream cone). By random, I mean unpredictable. Let me give an example. In population genetics, if you have two alleles (variants of a gene) that do not differ in their fitness effects–that is, the variants do not alter the survival or reproduction of the organism that carries either allele–then one allele will eventually disappear from the population by a process known as genetic drift. (Genetic drift has also been called a random walk). The point is that it is utterly unknowable which allele will disappear (although we do know that one will disappear). This is an instance of randomness.
Stochastic is best explained by its converse, deterministic. Flashback to algebra class, and imagine the equation Y = 2X. Suppose X = 50. Every time you solve the equation for Y, Y will equal 100. Not 99 or 101, but 101. It doesn’t matter when you solve this equation, or what equipment you use (unless it’s broken), Y will always equal 100. That’s a deterministic equation.
Now imagine the equation Y = 2X ± e, where e is some random small number. The ‘e term’ incorporates stochasticity into the equation. Depending on what random number is used to generate e, the value of Y will differ. Running the equation over will not necessarily generate the same value for Y (although it could). However, while we can not determine the precise value of Y, and thus this equation is not deterministic, we have a general idea of what that number will be. For example, if X = 50 and e is a random number between 1 and 5, we know that Y will range between 100 ± 5. This isn’t random in that we can approximate the term Y a priori, even if we can’t estimate its precise value.
This is relevant to biology (and all the sciences, for that matter) because, while it can be difficult to determine the exact outcome, we typically can incorporate stochasticity into our predictions–this is why technical papers on global warming, for example, incorporate confidence intervals. In the War on Science, those who oppose a given result often try to conflate randomness with stochasticity to undermine the integrity of science: the eggheads can’t give an exact result, so they must not know what they’re doing. In the context of evolution, the two terms are often confused by morons like Dembski who argue that complex structures could not evolve by “random chance.” However, evolutionary biology is a historical science. Given that there are pre-existing starting points, we can often approximate what will happen, even if we can’t be exact.