I know that you directed your question towards articulett, but when I see a sentence-long summation of a topic as complex as natural selection, I generally like to clarify.
Are you saying that what the selection pressure are (e.g., change in food supply or predation) are not random but how the act at the level of individual replicators to effect a change in allele frequencies is random in so far as when two individuals with identical collections of alleles are subjected to the same selective pressures one may survive and reproduce while the other my perish?
Essentially, yes. each generation of an organism in a stable environment will be more optimised for that environment, but there are many ways and
how this optimisation is performed is another matter.
A "fitter" organism is one with an increased chance of breeding, that is all I mean by "fitter".
An example:
Whether a peppered moth is eaten by a bird depends on whether it is seen by a bird. Better or worse camoflague might affect the probability of being seen, reducing the distance where there is a 70% chance of the bird seeing it, say, but whetehr the bird appears within this visible distance is essentially random, in that it has nothing to do with any trait that the moth has, given that it is in the same environment as potential predators. It can alter its behaviour to escape from some predators, but this will put it within the range of others.
This is for an individual moth. If you have many moths and many birds, one can begin to treat them as populatitions. One can then analyse differences in traits in the moths and see how these correlate with reproductive success.
In principle, a mutation arises in an individual, and this modulates the individuals reproductive chances. The probability of the mutation survivintg depends on the population and the reproductive chances of that population.
In a stable population I am assuming that there is on average one reproducing offspring per parent. A hypothetical mutation increases the reproductive success by 10%. If the average brood is ten per parent, with nine dying, then this mutation in one child will only have a 110%times10% chance of reproducing. If the mutated offspring survives to breed, then there is a better than 50% chance of the mutation surviving in at least one child.
I am assuming that this survival is modelled by a poission distribution, thus lambda will now be 1.1 as opposed to 1, for the non-mutated organism.
If the mutation survives for ten generations, then the mean breeding population is now 1.110 which is 2.5.., as opposed to 1 for the non-mutated offspring.
The more generations the mutation survives for, the more likely it is to survive further...
The chance of the mutation surviving will be the integral of the probable populations over the generations. And I can't be bothered to do the maths for that...
Of course, it gets easier in an oscillating population, for example lemmings. If the mutation occurs during a crash, it is very unlikly to survive, it it occurs during a boom, it is.
.
In a stable environment, the unpredictible aspects like predation and weather can still work as a selection pressure, if the events are frequent enough; they will then act to cause optimisation to that pressure.
However on geological timescales, the environment and thus the selection pressures change, and with mass extinctions, so many species are removed that many ecological niches are left unoccupied. Which niche is occupied first might preclude or open up other niches, and this, with the small initial populations would depend heavily on initial random starting conditions.
It is therefore quite likely that in such a stable environment, a mutation that affects the chances of reproduction is more likely to move away from "the optimum" than towards "the optimum". Thus most mutations that have an effect will be deleterious.
However, if the environment changes (e.g. the arrival of a new potential food supply like nylon) then the parent organisms are further from the "new optimum", and mutations are more likely to be beneficial.
New species are more likely to emerge to emerge when the ecosystem changes, and the old isn't so well adapted.
What is nonrandom about natural selection, it that over the generations there will be optimisation to the environment.