...I shall try to find time to read Dawkins' book. A cursory search for 'grandfather' in the book gives me the impression (correct me if I am wrong) that sharing the ancestor genes is from the paternal side, and no sharing from maternal grandfather who produced the mother of the child.
This is not true, and would be absurd as both father and mother contribute chromosomes to the foetus.
1) ultimately we descend from the primates, so aggressive behaviour is built in the genes of everyone;
and non-aggressive behavior as well. In the presence of alpha-male other members of the tribe behave in a submissive way. Further, there are species who have done away with aggressiveness within the clan for resolving conflicts, bonobos use sex for this purpose. So, aggressive behavior is not the only kind of behavior we humans have inherited from our ancestor species.
and yet when a child of normal parents is found to exhitbit cruel/aggressive behaviour right from childhood--and this is common--how does that child's genes suddenly acquire this trait in exclusion to the normal traits acquired in the ancestry chain for generations?
You answered this question yourself in the setup to the question, these come from eons of evolution. Wiki has a nice not too technical article on how off springs inherit genes from parents,
here. A small excerpt:
"The effects of this mixing depends on the types (the alleles) of the gene you are interested in. If the father has two copies for an allele for red hair, and the mother has two copies for brown hair, all their children will get the two alleles that give different instructions, one for red hair and one for brown. The hair color of these children depends on how these alleles work together. If one allele overrides the instructions from another, it is called the dominant allele, and the allele that is overridden is called the recessive allele. In the case of a daughter with alleles for both red and brown hair, brown is dominant and she ends up with brown hair."
• Thus, as I said, there is sudden disarry in the chain of immediate parents, who in this case with normal ancestry genes, has produced a child with aggressive genes!
First of all, I don't know whether there is just one particular gene sequence that produces aggressiveness. Do you have any citations for this. Even if this is so, the process by which the chromosomes combine to form a foetus is a complex one, many factors play a part. In this process some gene mutation can take place and the off spring can come to possess traits that were not present in either parents. This is a part of nature, nothing supernatural about it, no invisible karma coming in and playing tricks with the gene.
• How does science actually verify Dawkins' proposition of sharing genes from generations up in the ancestry chain? In fact I should ask, how does science empirically know from an examination of the genes when a child is born, that the child will have such and such traits?
There are certain traits that can be very precisely predicted. Sickle cell anemia is one. Eye color, baldness, etc. are traits that be predicted by looking at the genes of the parents. Any trait that arises out of gene mutations cannot predicted as such mutations are caused by a myriad of factors. Again, these are result of natural processes, not some poorva janma karma.
• So, the commonly seen facts of an aggressive child in a chain of perfectly normal ancestors up some generations, or an autistic child, or a child born with physical deformities, are all IMO the results of pUrva janma karma and not ancestory genes.
Well, your opinion is formed on the basis of faulty understanding of the facts and an allegiance to Hindu Darma.
"Besides, this is irrelevant to the main thesis that I-awareness is a brain state", you said. Well, this thread is more about karma than I-awareness.
Okay!
02. The 'significance' of a serial killer and his helpless victim is that if the former's behaviour is in his genes, I asked if the latter's helplessness in falling a victim is also in the genes. If DNA can give murderous behaviour in one person, why can't the victim's DNA give their timid and helpless behaviour?
Even if this is so, so what? You are assuming that it was helplessness that made the victims to be victims, not quite.
03. I did not mean physical fitness, but the evolution of consciousness, which, you will agree, is the most developed in man. This is man's vertical evolution from his primate cousins.
Alright!
• The horizontal evolution is the mental behaviour which is not at all uniform in man as it is in animals.
That is not Evolution as in Darwins Theory of Evolution.
As I said, they hunt and kill only for food, mate only for procreation and behave normal in their other activities of life. For example, a cat does not kill a butterfly for the sake of it, whereas a human child does it just like that.
Non-sequiter!
• If the horizontal evolution is thus aberrational in man, it should be due to his mind and desire and not his genes. This was my point. It is another issue, however, if this mind is purely physical or not.
There is no such thing as horizontal evolution. Genes do not think, it just has the code to create the chemicals for certain actions to take place. It is the brain that thinks, that thinking state is part of what gets understood as mind. All these have basis in the genes.
• So the point is love and compassion are not traits inherited from the genes, but acquired in life using the mind through the resulting experiences. Surely, these traits will be carried over in the next birth of the person, rather than percolate down the ancestory chain.
Love and compassion are rooted in the genes just as much as aggressive behavior. Snake mothers have no love for her baby and leaves them to fend for itself. This is so because snake-mother love bestows no survival advantage to the baby, it is unnecessary. However, there are many species, including humans, in which the babies cannot survive without the protection of their mothers. So, babies with unloving mothers perished in larger numbers compared to babies that received mother's love and protection. Over time the gene responsible for love came to dominate and ultimately almost eliminate unloving mother. The postmortem depression must be a holdover from those times of unloving mothers. All this is rooted in the genes, not some supernatural karma.
The poorva-janma Karma theory has absolutely no basis in fact. Only the religiously motivated argue in in its favor and offer nothing by way of evidence. The field of genetics is a well established scientific field and their copious findings are facts, verifiable facts, and humans have benefited enormously from their research. Gene theory offers tangible benefits, Poorva-janma karma theory offers us misery and oppression.
Cheers!
our problems - the problems of hinduism in a changing world. 
