Let's see if we can figure this out from first principles. Limiting ourselves to biological evolution, evolution needs a few things to work in practice:-
-a mechanism of inheritance. Genes in our case. Consider stones. Stones don't have genes. Stones don't evolve (biologically, that is. I know a pebble back in my village river that somehow manages to accumulate little pebbles around it that are more smooth. I think it's cheating.)
-one or more heritable characteristics. For instance, Lactose tolerance. Our ancestors couldn't stomach milk--until about 30,000 years ago. Lactose tolerance evolved, multiple times in various groups. Most of us can now digest milk because we have inherited the necessary genes from our ancestors. Some of us have't inherited the gene and suffer from indigestion when milk (lactose, to be precise) gets in.
-selection pressures. For instance, marginally better survival of babies with milk tolerance (this is presumably how we evolved lactose tolerance)
Take away one of these pre-conditions and biological evolution will hit a wall. So, it appears to me that evolution could stop if one of the above conditions is not met.
Digression: Here's an idea for a science fiction story. Imagine a civilization that has deliberately and methodically removed all the above evolutionary pre-conditions, in other words, hey presto, an Utopia! All the saints and philosophers of this Utopia have committed sepukku (cut-me-tummy, japanese style)--saints, because they understood gods were not needed to attain perfection; philosophers, because they lost their vocation. The inheritors who remain face a conundrum. They are perfect, and they are absolutely miserable. Who shall rock the boat and release their kind from the irony of it all...
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Your story sounds a little like Huxley's 'Brave New World'.
The problem with the conditions is that the method of inheritance of eukaryotes is inherently inefficient and prone to mistakes (genomic dublications, loss, mutation etc).
This means even if you started from a position of every single member of the population having the same homozygous alleles variation would arise in the next generation. Once you have variation then evolution will occur. Finally it is hard to think of any situation where the environment remains unchanged over long periods of time - thus this environmental variation will allow for differing selective pressures among the newly derived biological variations.
It seems hard how either one of the conditions could disappear.
Selection pressures and variation are always going to be present. As for mechanism of inheritance, a lot of times that's dictated by basic physics and chemistry. And of course, stones do evolve! For instance Alexander Graham Cairns Smith posited the evolution of silicate minerals through defects (variations) and selection pressures (ability to withstand weathering)
Random genetic drift is a major mechanism of evolution. It's described in all the biology and evolutionary biology textbooks. It's probably the main mechanism of evolution if you just count all known instances of evolution.
Random genetic drift is not adaptation. If you completely remove all selection pressures then you are still going to get lots of evolution. If you think about human populations, for example, there are very few adaptive mutations fixed per generation but every generation there are 130 nearly neutral alleles fixed by random genetic drift.
Sorry for the criticism but I'm on a campaign to teach everyone the correct concepts of evolution.
Just remember this: "natural selection" is not a synonym for "evolution."
Larry, thank you for the interesting comment. I wasn't aware of the potential importance of drift.
For the benefit of other readers, let me quote from your talk origins page a passage that captures the key point nicely: "The key question at stake is whether the immense genetic variety which is observable in populations of all species is inconsequential to survival and reproduction (ie. is neutral), in which case drift will be the main determinant, or whether most gene substitutions do affect fitness, in which case natural selection is the main driving force. The arguments over this issue have been intense during the past half- century and are little nearer resolution though some would say that the drift case has become progressively stronger. Drift by its very nature cannot be positively demonstrated. To do this it would be necessary to show that selection has definitely NOT operated, which is impossible. Much indirect evidence has been obtained, however, which purports to favour the drift position. Firstly, and in many ways most persuasively is the molecular and biochemical evidence..." -http://www.talkorigins.org/faqs/genetic-drift.html
Sure evolution on Earth could stop.
I suppose that there is at least some finite, but very small chance that some astronomical process could utterly destroy the Earth (ignoring the Sun's evolution which will eventually cause problems....).
Other disasters that actually take out life on Earth completely, I dare say the answer to the question "Could Evolution Stop?" is "Not a chance."
You're also neglecting that selection pressures occur at multiple levels: biochemical, organelle, cell, organ, organism, society, species, ecology, and biosphere.
Evolution is as easy to stop as the second law of thermodynamics.
I suppose that there is at least some finite, but very small chance that some astronomical process could utterly destroy the Earth (ignoring the Sun's evolution which will eventually cause problems....).