Its more like your first example. Mutations happen all the time and mostly have no affect on reproductive success or any non-negligible affect on the allele frequency of the population. The environmental affects come after the mutations and determine which mutations ”succeed’ or ”fail’.
then that family line will soon dominate the population, until all members of the population posess the mutation
Even if this happened it would not be speciation. Speciation requires a separation from the parent population, either geographically, by some morphological difference that prevents reproduction, or something else. If the mutated population is not separated, but ends up dominating the parent population, then that population has evolved but no speciation has occurred.
An environmental change occurs, 'encouraging' mutations across the population.
Mutations happen all the time, randomly. I think it is
possible for the environment to encourage mutation, by nuclear radiation or something, but I don’t think this is something that really promotes speciation.
Over time, the beneficial mutations are pooled together to create new species.
No, some kind of seperation is needed.
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