First, I must confess that while I do have a BS in a science it was not biology let alone a sub-field that looked more specifically at genetics.
Second, from some other discussions here (and elsewhere) I think it would be extremely helpful to have something here that helps people to understand just how the procreation process works from a genetic standpoint.
I am not sure if a discussion thread is the best venue for it, but let's start here.
I also am not sure about how technical we might wish to get, but there will have to be some use of technical terms. Also, I do not wish to condescend to anyone, nor do I wish to pander to anyone. However, to make it as easy as possible for people to understand the more technical aspects, I think the discussion should start with the most basic aspects of DNA and living organisms. Different kinds of organisms (i.e. bacteria, viruses, fungi, plants and animals) have different cell structures and genetic materials. Some bacteria and/or viruses, for example, use RNA as the primary encoding genetic material and not DNA. Also, many, if not most or all, multi-cellular animal organisms do not have all of their genetic material within a single sub-structure of the individual cells. The cell structure for mammals especially has sub-structures in the cytoplasm (which is something like a soup). The cytoplasm is outside of the cell nucleus but inside the cell wall/membrane. Some of those sub-structures are ribosomes and some are mitochondria. There are other sub-structures as well, but, as far as I know they are not important (at least not directly) to a discussion of the genetics. What is important for us, is that the primary genetic material (DNA for us) necessary for replicating individual cells and for procreation is not all stored in the cell nucleus. The majority of it is. That would be the 23 pairs of chromosomes. The rest is in the mitochondria in the cytoplasm. There are theories as to why the mitochondria have their own DNA. I do not think we need to get into that discussion.
Let's look at the mitochondria in a cell's cytoplasm. Mitochondria perform essential funtions in all of our cells, including the cells neccesary for procreation (that is in the spermatzoa and in the ova). Somehow, during the fertilization of an ovum by a sperm cell (or shortly after) the mitochondria of the sperm is destroyed. [ Note: I have read something recently about some research which indicates there are instances of some of the mitochondria of sperm cells surviving this process, but if it does occur, it does so very infrequently. Also, if it does occur, it will affect the outcomes of mitochondrial DNA testing. ] This means that mitochondria, and therefore, the mitochondrial DNA in our cells is contributed solely (reference the Note above) by the maternal line through the mitochondria of the fertilized ovum. This why mitochondrial DNA testing is done to confirm maternal lines.
Now for the majority of the DNA necessary for our procreation and cellular replication. The 23 pairs of chromosomes in the cell nucleus are to be categorized as 1 pair of sex chromosomes (the famous X- and Y- chromosomes) and 22 other pairs of chromosomes. Women have 2 X-chromosomes. Men have 1 of each (disregarding rare cases where the male of a species gets 1 Y- and 2 X- chromosomes. There are usually very debilitating diseases associated with these cases.) How do they get passed to the next generation and thereby determine the sex of the offspring? In a woman's ovaries, the cells which produce the ova, split the pairs of chromosomes when producing the daughter cells (the ova). Now here's a finer point about which I am unsure. I do not currently know if in this process, all ova get the exact same X-chromosome or if some get the 1 contributed by the mother while others get the 1 contributed by the father. Either way, each ovum (normally) only has a single X-chromosome. In Men, the pre-cursor cells in the testes also split the pairs of chromosomes when producing the spermatozoa. Some of the sperm will carry an X-chromosome. Some will carry the Y-chromosome. When a sperm with an X-chromosome fertilizes an ovum, the resulting embryonic cell has 2 X-chromosomes and if it develops properly produces a female. When a sperm with a Y-chromosome fertilizes an ovum, the resulting embryonic cell has 1 X- and 1 Y- chromosome, producing a male.
Since for these processes, the splitting of the pairs of chromosomes by the pre-cursor cells is a random process, the percentage of sperm with Y- chromosomes and those with X- chromosomes should be theoretically 50% each. The fertilized ova should therefore be 50% male and 50% female. All statistical processes do not match the overall statistics at any given time, but should tend toward those numbers, provided that there is not some other process at play ( such as, for example, cultural pressures to produce males and not females leading to the abortion of more female fetuses than male fetuses.) Now, the question this suggests is: what does this mean for genetics?
One thing it means is that the Y-chromosome DNA tests can only be used to verify or disprove DIRECT patrilineal descent/ancestry, since only the males carry the Y-chromosome. A female does not have Y-chromosomes to pass on. So, if one gets a Y-DNA test done and wishes to match to a male ancestor, then they must look for the match with a MALE. That may sound a bit redundant, but let's say that someone thinks that there may have been an NPE, a Non-Paternal Event - i.e. that at some point the true biological father of an ancestor was someone other than what the historical record says it was, they should be looking for a DIRECT MALE descendant (strictly paternal line) from the suspected true ancestor to have had offspring with the known maternal ancestor for comparison testing and not a FEMALE ancestor who was a descendant through a direct paternal line of the suspected Y-DNA source to have had a child or children from the historical biological father. Y-chromosome DNA is not crossed in any fashion with the DNA of an X-chromosome or any of the other chromosomes that a maternal ancestor carries.
Some DNA does get mixed. This occurs with the other chromosomal pairs. This is where the autosomal DNA testing comes into play. It may be used to help locate biological relatives from ANY and ALL lines. It does, however, become much less reliable the further removed the relationship due to this mixing.
Additionally, something to remember when discussing haplogroups. There a 2 distinct sets of haplogroups to discuss. One set of haplogroups is for the mitochondrial DNA. The other is for Y-chromosome DNA. THEY ARE NOT IDENTICAL. I am unaware of the status of X-chromosome research and also for that of the 22 non-sex chromosome pairs. There may be efforts with some of the genomic studies to determine if any haplogroups exist for these. I do not follow this research religiously. I suspect that one would be able to determine haplogroups for X-chromosomes, but the problem in using them is that of trying to determine how to make use of that. Since a woman has 2 X-chromosomes, how can we be sure which one comes from the mother and which from the father. For males, we can be sure that the X-chromosome comes from the mother, but how can we be sure which of her parents contributed that X-chromosome to her. Any such research would most likely require larger samples with far more detailed tracking of the ancestry of the contributors to be able to begin to sort that out reliably.
I am not going to get into the statistics of probability of matching a particular person as having a common ancestor within so many generations, except to say that my understanding so far is that the statistics are a little different depending on whether the test is Y-DNA, mitochondrial or autosomal. It also depends a great deal on the number of marker sites tested for comparison purposes. I have not had a separate stand-alone statistics class (although some of the classes I have had used statistics and probabilities to a large degree), nor have I, as I already stated, followed this research religiously. For that reason, I have not yet got my head around the rates of mutation for different marker sites on Y-chromosomes and mitochondrial DNA or on other chromosomes and how those rates of mutations combine with the random statistics of the mixing of chromosomes from parents during the production of sperm and ova to predict the likelihood of a common ancestor within a certain number of generations.
I apologize for such a long post. But, I think the way I have presented the basics of the topic as best as I currently understand them is the best way to lay the groundwork for the discussion. Hopefully, some other person or persons here can correct any mistakes I may have made in this initial post and provide more detail to help us all understand this topic better. Especially since I think that the use of DNA testing for genealogical purposes is almost definitely going to continue to increase.