Evolution without natural selection

I find the idea that evolution is possible without natural selection fascinating!

Suppose that there is a fixed number of species with equal number of male and female and exactly the same length of life for all species. Each pair produce two offspring male and female keeping the perfect balance of the whole population. Now is the question: is evolution possible in this scenario? One answer is no, because there are no natural selection and no preference is given to one carrier of genes before another.

If genes are taken from the parents in exactly random way then each parent pair pass 75 per cent of their genes to their offspring, because it is 50 percent from each parent to each child, so 25 percent is shared between two offspring. It means that with each generation a quarter of all genes are lost. However due to genes variety and enough repetition within the whole population, the number of distinct genes may not be decreasing. If there are random mutations in genes the variety can increase. In the other case when passing genes is not fully random, less than 75 per cent is being passed, so the washing out of genes is even faster.

Suppose however that there is a mechanism which marks genes of the individual as better or worse. If two genes one from each parent fight for the place to be in the descendant based on their marked value, then better genes are passed to the next generation and worse genes will be lost. In this case the natural selection happens on the level of genes and not on the level of species. Overall trend is that each generation has better genes even that no preference is given to any creature during its life.

Obviously there are two questions here. First what is that mechanism which makes genes to be marked and compete? And second, what means a better gene? Or in other words, how the organism decides which gene to reward and which to punish? Let them to be open. What is interesting is that evolution happens in a completely perfect and stable environment for species.

If something like this happens in reality, the main reason for this probably is the elimination of undesirable mutations in genes.