Not that long time ago scientists have established that we all share one mother (and and one father, then). The interesting thing is that Eve was living 100 thouthands years earlier than Adam. So they could not have sex with each other and even see each other. How is this possible? The answer is that there are competing pieces of genome: some people have one allele in that locus of genome, others carry another. It can happen that one allele evicts all the competitors. So, there was a women which had a mutation in her mitochondrial DNA and this piece of DNA started to spread over the population so that 100 000 years later all women had it (others died without descendents).
You may think that our mother have got very evolutionary advantageous piece of DNA, which have managed to monopolize all the population because it was so efficient. I have considered however what if no allele has evolutionary advantages over the others. That is, they all are equally likely to be selected from the population for reproduction. We start with all parents different. Will any of them monopolize the population, eliminating all competitors?
The simplest case to permit elimination of some genes is to maintain a fixed-size population. N parents produce N offspring every generation. These N kids are parents for the next generation. You do it by sampling the (parent) population N times (with replacements, sinble parent can be picked any number of times; otherwise, population of children will be a copy of the parents). If some parent is not sampled, his allele ceases to exist in the future. You see, it seems like a converging process. You can loose some alleles at every generation so that chance will reduce the diversity the same way as gas molecules tend to fill up all the tank: there is more molecules to move from dense area into the vacuum than vice-versa.
It seems inevitable now that you will loose all diversity over time even if competitors have no advantages over each other. The loss of diversity is however slows down as you get a much more individuals than alleles. It is very likely that one of 100 different parents will not be sampled by 100 random draws. Yet, if you have a population of 50 fathers of one kind and 50 of another kind, and sample the box of them 100 times at random (two companies remains on the market and 100 people order the services from both at random) it will be very unlikely that no company remains without orders and thus disappears. On the other hand, it may be like a random walk - your company reduces a share on the market, it becomes less popular (less parents of that kind), so, it is less likely to be chosen on the next round so on and on and the less popular provider disappears. So, what is the speed of the diversity loss?
Simulator suggests that average extinction time is no longer than 4 population size: