@sygarte, all that “random” means is that the mutations are not entirely predictable from the modeler’s point of view. They can follow a pattern. They can even be related to fitness, but the would still be “random”, if we don’t know precisely where they will happen ahead of time. They can be deterministic. They can be intelligently guided. The only claim is that the model itself can’t fully predict them.
“Random” is an intermediate term between “chaos” and “determinism” because it can include patterns, or a distribution. In fact, it is hard to envision a random variable that does not have some sort of pattern. A good description of “random” is here:
In probability and statistics, a random variable , random quantity , aleatory variable , or stochastic variable is a variable whose possible values areoutcomes of a random phenomenon.[1] More specifically, a random variable is defined as a function that maps the outcomes of unpredictable processes to numerical quantities (labels), typically real numbers. In this sense, it is a procedure for assigning a numerical quantity to each physical outcome. Contrary to its name, this procedure itself is neither random nor variable. Rather, the underlying process providing the input to this procedure yields random (possibly non-numerical) output that the procedure maps to a real-numbered value.
A random variable’s possible values might represent the possible outcomes of a yet-to-be-performed experiment, or the possible outcomes of a past experiment whose already-existing value is uncertain (for example, due to imprecise measurements or quantum uncertainty). They may also conceptually represent either the results of an “objectively” random process (such as rolling a die) or the “subjective” randomness that results from incomplete knowledge of a quantity. The meaning of the probabilities assigned to the potential values of a random variable is not part of probability theory itself but is instead related to philosophical arguments over the interpretation of probability. The mathematics works the same regardless of the particular interpretation in use.
Notice that even if mutations are not independent of fitness, they would still be modeled as a “random” variable, because we cannot fully predict them a priori. In fact, even targeted edits with CRISPR would be modeled with a “random” variable, because these edits (even though they are engineered) are not entirely predictable. We know there are patterns to mutations too (transitions > transversions), but this also does not make them non-random. It just means that they follow a distribution biased towards transitions. They are still “random.”
The whole question of “independent” of fitness (or not) is a red herring, in my opinion. First, in a precise sense, I’m not sure it is true. Rather, if you look at the experiments from which it is derived (The Luria and Delbruck Experiment), it just means that beneficial mutations (in a particular context) are not induced by the environment, but preexist selective pressure. Even this is merely a rule of thumb that is not strictly true (e.g. look at the immune system).
Of course, there does need to be more mathematically precise language through out biology. EES is not taking us that direction, but is clouding the water even further by investing “random” with additional meanings that are just not valid. It would be easier to just remember the standard definition of “random” in modeling. It includes no metaphysical baggage. It does not require a grand rethink of biology, and might even make for more clear explanations of evolutionary science.
Does that make sense @sygarte?