I understood the paper to be saying that living things can only tolerate a certain amount of mutations and therefore risk extinction.
That's an implication of the paper. If the mutation rate were so high that individual proteins were accumulating deleterious mutations faster than they could be purged by selection, then yes, that species will go extinct. I know of no such species, though. Measured mutation rates are quite tolerable.
I have posted a number of papers along these lines. But it is the accumulation of perhaps small amounts of slightly harmful mutations that are doing the damage.
But that's something that isn't actually happening.
I am not saying there is a specific amount of mutations that bring a creature to ruin but that random mutations are basically an error in what is already working good and the fact that the DNA has a mechanism to correct those errors shows that mutations are not meant to be something that can create fitter and more complex life.
Mutations aren't meant to be anything, as far as we can tell. They're inevitable errors. Most of them either do nothing or damage the organism, while some of them improve it. Those are simply facts.
First off I noticed you did not address what was said about non-random directed mutations being a source of variation rather than random mutations which is the main source of variation for neo Darwinism.
I know of only one class of mutations that are non-random (in the sense that evolutionary biology means), and I doubt those are mutations that you're thinking of.
As seen with recent research humans are accumulating many slightly harmful mutations and natural selection cannot keep up in purging them out of our genomes so therefore we have a building number of diseases.
That's completely wrong. No recent research says that humans are accumulating slightly harmful mutations. Because our population size has soared in recent millennia, we are actually reducing the number of deleterious mutations that we carry.
So you are saying that apart from smaller populations slightly harmful mutations do not accumulate.
Correct.
From what I have read it seems they do and there are different reasons why natural selection may not be able to weed them out. For example
Despite the current status as the dominant organism on earth, the human species is confronted with substantial mutational challenges imposed by at least three baseline genetic features: (i) a relatively high per-generation germline mutation rate at the nucleotide level; (ii) a further inflation in the mutational rate of production of defective alleles associated with aspects of gene structure; and (iii) a large cumulative burden of somatic mutations imposed by a relatively late onset at maturity.
Rate, molecular spectrum, and consequences of human mutation
Every time a cell divides, genetic errors can occur, leading to variations in the DNA sequence that may proliferate and—in some cases—cause disease. Now that genetic sequencing and other technologies have made it easier to recognize mutations that occur in only a subset of cells, researchers are finding more and more harmful mutations hidden among unaffected cells.
Harmful mutations can fly under the radar
Neither of those says anything at all about mutations accumulating over multiple generations. They're just talking about the rate of deleterious mutations.
The relentless accumulation of deleterious mutations is primarily due to the existence of un-selectable “nearlyneutral” mutations, but the genetic load problem is greatly amplified when mutation rates are high. Intensified natural selection only marginally slows the accumulation of deleterious mutations.
http://bioinformatics.cau.edu.cn/lecture/chinaproof.pdf
That's wrong. As I suspected, it's from Sanford, who's a creationist who has some odd ideas about population genetics.
Even if we believed that we would need a multitude of beneficial mutations at only 1% of all mutations to get the level of variety and complexity we have today. If that's the case we would also need an overwhelming amount of harmful mutations as well. Under normal circumstances this level of mutations is associated with sickness, malfunction and cancer let along creating something fitter.
The deleterious mutations come and go, every generation. The beneficial mutations stick around (well, some of them anyway). This filtering process is highly effective.