Can you elaborate? maybe give an example.
No need for examples. It’s a logical necessity. If there are such things as advantageous mutations, and they constitute some proportion of all possible mutations, then sampling randomly from all possible mutations must eventually arrive at an advantageous one or two. Further, if a mutation is deleterious, then a back mutation at the same site must also be advantageous.
Now what’s your evidence of a bias such that advantageous mutations happen more often than expected by chance?
Not the best example because studies show that they can predict the distribution of mutations:
“A central tenet in evolutionary theory is that mutations occur randomly with respect to their value to an organism; selection then governs whether they are fixed in a population. This principle has been challenged by long-standing theoretical models predicting that selection could modulate the rate of mutation itself1,2”
Addressed above
We would expect a lower rate in highly expressed genes and in those undergoing stronger purifying selection.
Not true. You have misread again. Modulating the rate of mutation doesn’t change the distribution of mutations. And please, no more unattributed quotes.
An interesting paper - you should read it sometime.
In that case, I don’t understand this comment. I explained how we are going to get advantageous mutations regardless of whether mutations end up being beneficial, cancerous, or neutral.
Now, if you are suggesting bias towards creating new function in regards to beneficial mutations, then this would not matter. As I said before, the purpose would not solely be genetically engineering new function in an environment. Instead, it would be to edit and limit the amount of errors the cell makes in maintaining existing function. The studies I provided show this.
Can’t you at least try to use words so that they have meanings? “Advantageous” is a synonym of “beneficial”. Advantageous mutations, by definition are neither cancerous nor heutral. Whatever are you trying to say here?
Not according to my definition because my definition is based on studies that show how even cancerous or neutral mutations can be beneficial to the organism one way or another.
In what alternate universe is cancer good for you?
Your definition is not clear, and you can’t expect anyone to understand you if you keep making up your own definitions, especially if you neglect to say that you are, and what they are.
A mutation can increase fitness even if it also increases the risk of cancer.
I suppose in theory a tumour could increase a male animals weight and give it an advantage in competition with other males over mating rights.
But the latest claim that “neutral mutations can be beneficial” (with studies to back it up!) is too ridiculous to bother with.

A mutation can increase fitness even if it also increases the risk of cancer.
A ‘cancerous mutation’ surely goes beyond the mere risk of cancer to the reality of it. Otherwise it would surely be termed ‘pre-cancerous’ or similar.

A ‘cancerous mutation’ surely goes beyond the mere risk of cancer to the reality of it. Otherwise it would surely be termed ‘pre-cancerous’ or similar.
Given the source, who could possibly know what (if anything) was actually meant?

Given the source, who could possibly know what (if anything) was actually meant?
Yes, but if we, unprompted, go beyond the plain meaning of words, and assume that the words do not follow their plain meaning we end up in a meaningless void, where even any attempt at communication is fruitless.

Yes, but if we, unprompted, go beyond the plain meaning of words, and assume that the words do not follow their plain meaning we end up in a meaningless void, where even any attempt at communication is fruitless.
I was attempting to work out what the poster might have meant by the words in question. Why do you think this is worth arguing about?

In what alternate universe is cancer good for you?
The vast majority of mutations in regions that do encode proteins but are deleterious appears to be fine-tuned to lower the risk of harmful genetic changes. Moreover, mutations are guided by both the physical properties of the genetic code and the need to preserve critical protein function
Evidence of non-random mutation rates suggests an evolutionary risk management strategy | Nature
The harmful mutations that do arise ensure the death of individuals so that resources are available for the young among prey and predators because too many predators or prey can cause a collapse of the ecosystem. In other words, it prevents greater harm from those organisms.

But the latest claim that “ neutral mutations can be beneficial ” (with studies to back it up!) is too ridiculous to bother with.
The Toddler gene is an almost perfect example of this:
"Toddler is annotated as a non-coding RNA in zebrafish ( ENSDARG00000094729 ), mouse [ Gm10664 ; also called Ende (10)], and human ( LOC100506013 ) (fig. S2) and is present in two lncRNA catalogs (9, 11); however, it contains a 58–amino acid ORF with a predicted signal sequence and high conservation in vertebrates, including human (Fig. 1D and fig. S3). Sequence comparisons with the highly conserved C-terminal portion did not identify homology to any other known proteins, raising the possibility that this gene encodes an uncharacterized embryonic signal.
Six lines of evidence indicate that toddler is translated and encodes a secreted peptide."

we end up in a meaningless void, where even any attempt at communication is fruitless.
In any thread begun by a small, colonial mongoose, that’s where we start.