Is natural selection actually random?

Question

In the Theory of Evolution, two main factors take place:
One is random, which are the different mutations that organisms' DNA suffer. This process adds genetic variability to a given population.
The other one is not random, which is natural selection. It is not random because it will only select  those organisms which are better capable of surviving to the conditions of their environment.
Most likely I am wrong and I would like to be corrected, but I was thinking that, since natural selection depends on mutations and the conditions of the environment, and since those conditions can be formed by random processes, wouldn't it make natural selection as actually random?
I mean, this is probably an over simplistic analogy, but take a group of mammals which suffer a great series of mutations in a short period of time, and separate into two species of mammals: one group of animals with hair and the other group has no hair at all. Suddenly, one day starts to snow. We could expect that the second group would most likely go extinct, while the mammals with hair would survive. Since the weather is based on random processes and since natural selection in this example would be based on the mutations that the animals suffered and the weather as well, wouldn't natural selection be a fundamentally random process?

user438383 · Answer

You are right in a sense. The processes which generate mutations in an organism are stochastic (not quite exactly random, but in most organisms they are effectively random for all intents and purposes). In terms of population genetics, it is considered that mutations occur randomly across the genome and have an equal probability of occurring at a given base pair.
The environment is also random/stochastic in the sense that it occurs mostly independent of mutations which have occurred. Whether or not it is cold one year is independent of the mutations which have occurred within an organism. (Actually that's not quite correct since organisms can generate their own environmental niches and evolve according to them, but I think that is beyond the scope of this question).
What is not random is how the frequency of genetic variants respond to different environments. This is natural selection. Over the long run, we expect genetic variants which increase the fitness of an organism within a given environment will increase in frequency and vice versa. There is a large body of theory and evidence which predicts how a particular variant may change in frequency in response selection of a particular pressure.
As @jamesfq correctly points out, a nice example of selection being non-random on the macro-scale is convergent evolution. For example, aquatic animals such as fish, certain mammals (e.g. Dolphins) and Amphibians and Dinosaurs have independently evolved streamlined bodyplans in order to conserve energy when moving through the water.

Is natural selection actually random?

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