Does a 6,000-year-old earth match the findings of modern science?
No
Lyell discovered that the earth was old before Darwin and modern science confirms it.
Thus, mitochondrial DNA differences among modern individuals within a created “kind” trace back to the maternal ancestor of the kind.
"Kind" is not a scientific word. It's something pulled out of the KJV and warped into the meaning YECs use it for, in order that they can acknowledge the overwhelming evidence for small-scale evolution without admitting that it's the same process as large-scale evolution, just over a shorter period of time.
If kinds have existed on this planet for millions of years, then they should be quite genetically diverse. In contrast, if their origins trace back only 6,000 years, then they should be more genetically homogeneous.
Life on earth is genetically diverse. I guess in order to stick with this story though, if something is too diverse they just say it's a different "kind". For example... foxes and wolves, YECs will say it's the same kind. Foxes, wolves, bears, weasels and cats (All in Carnivora), young earth creationists say they're different kinds, regardless of the fact they are genetically close and have Carnivora physical traits that set them apart from other life on earth.
Secular scientists have spent many years developing the equations for estimating DNA differences over time.
It's used to determine when two different species shared a common ancestor.
Secular scientists have measured the mitochondrial DNA mutation rate for four species—humans, fruit flies, roundworms, and water fleas. The Bible puts the origin of each of these about 6,000 years ago, and we rounded it up to 10,000 years.
Yeah, why not round it up by about 67%, what difference in accuracy could it possibly make?
Plugging these numbers into equation (1) reveals a sharp contrast between the creation and evolutionary predictions (Figures 1 and 2). For example, the measured mitochondrial DNA mutation rate for humans is, on average, ~0.00048 mutations per year.4,5 Multiplying 0.00048 by 2 and by 10,000 years yields a prediction of about 10 mutations after 10,000 years of existence. Conversely, multiplying 0.00048 by 2 and by 180,000 years yields a prediction of about 174 mutations after 180,000 years of existence.4,6
Comparing these predictions to the range of actual human mitochondrial DNA diversity shows a striking result (Figure 1).4 On average, human mitochondrial DNA sequences differ at 10 positions. The biblical model predicts a range of diversity that accurately captures this value. In contrast, the evolutionary timescale (and, by extension, the old-earth creation timescale) predicts levels of genetic diversity that are 12–29 times off the real DNA differences that we see today (124–290 mitochondrial DNA differences versus 10).
The equations are talking about average mutation rate over time, but there are times when there is more selection pressure or less selection pressure. The claim that evolutionists somehow believe evolution happens at a steady pace all along the way is a gross misunderstanding. Evolution tends to move faster when new niches open up to exploit due to extinction of those creatures previously filling those roles. It might slow down if the creature is well-suited to its environment and new mutations provide no selective advantage. A mutation is only "good" or "bad" in the context of the environment it's in. A mutation for thicker hair would be good in a cold climate up to a point, but in a hot climate it would be bad. In a temperate climate, it might be neutral.
they would need to mutate only once every 21,000–36,000 years and consistently so for millions of years (Table 1). This incredibly slow rate is completely counter to the actual mutation rates observed in genetics; in fact, rates this slow seem biologically impossible.
Are they really this dumb that they don't realize that this is an argument in favor of evolution? If all evolution needed was a positive mutation to spread once ever 30k years or so, then all those arguments YECs bring up about how most mutations are bad are thrown out the window.
I think we all know that mutations do happen more often than that, and the good ones are more likely to be spread through a population through natural selection. Every offspring has mutations from its parents (most of them are neutral) and sexual reproduction mixes things up even more by allowing the offspring to receive genetic information from both parents, increasing the likelihood of inheriting a good mutation and making it more likely that such a good mutation will spread through the population.