(Genesmanship) Kin Altruism and Parental Care

(Genesmanship) Kin Altruism and Parental Care

by : Aria Ratmandanu       

           Suppose you contain one copy of the gene G. You must have  received it either from your father or from your mother (for convenience we can neglect various infrequent possibilities — that G is a new mutation, that both your parents had it, or that either of your parents had two copies of it). Suppose it was your father who gave you the gene. Then every one of his ordinary body cells contained one copy of G. Now you will remember that when a man makes a sperm he doles out half his genes to it. There is therefore a 50 per cent chance that the sperm that begot your sister received the gene G. If, on the other hand, you received G from your mother, exactly parallel reasoning shows that half of her eggs must have contained G; once again, the chances are 50 per cent that your sister contains G. This means that if you had 100 brothers and sisters, approximately 50 of them would contain any particular rare gene that you contain. It also means that if you have 100 rare genes, approximately 50 of them are in the body of any one of your brothers or sisters.”

                You can do the same kind of calculation for any degree of kinship you like. An important relationship is that between parent and child. If you have one copy of gene H, the chance that any particular one of your children has it is 50 per cent, because half your sex cells contain H, and any particular child was made from one of those sex cells. If you have one copy of gene F, the chance that your father also had F is 50 per cent, because you received half your genes from him, and half from your mother. For convenience we use an index of relatedness, which expresses the chance of a gene being shared between two relatives. The relatedness between two brothers is 1/2, since half the genes possessed by one brother will be found in the other. This is an average figure: by the luck of the meiotic draw, it is possible for particular pairs of brothers to share more or fewer genes than this. The relatedness between parent and child is always exactly 1/2. It is rather tedious going through the calculations from first principles every time, so here is a rough and ready rule for working out the relatedness between any two individuals A and B. You may find it useful in making your will, or in interpreting apparent resemblances in your own family. It works for all simple cases, but breaks down where incestuous mating occurs, and in certain insects, as we shall see.

               First identify all the common ancestors of A and B. For instance, the common ancestors of a pair of first cousins are their shared grandfather and grandmother. Once you have found a common ancestor, it is of course logically true that all his ancestors are common to A and  B as well. However, we ignore all but the most recent common ancestors. In this sense, first cousins have only two common ancestors. If B is a lineal descendant of A, for instance his great grandson, then A himself is the ‘common ancestor’ we are looking for. “Having located the common ancestor(s) of A and B, count the generation distance as follows. Starting at A, climb up the family tree until you hit a common ancestor, and then climb down again to B. The total number of steps up the tree and then down again is the generation distance. For instance, if A is B's uncle, the generation distance is 3. The common ancestor is A's father (say) and B's grandfather. Starting at A you have to climb up one generation in order to hit the common ancestor. Then to get down to B you have to descend two generations on the other side. Therefore the generation distance is 1 + 2 = 3.

              Having found the generation distance between A and B via a particular common ancestor, calculate that part of their relatedness for which that ancestor is responsible. To do this, multiply 1/2 by itself once for each step of the generation distance. If the generation distance is 3, this means calculate 1/2 × 1/2 × 1/2 or (1/2)³  If the generation distance via a particular ancestor is equal to g steps, the portion of relatedness due to that ancestor is (1/2)^g. 

          But this is only part of the relatedness between A and B. If they have more than one common ancestor we have to add on the equivalent figure for each ancestor. It is usually the case that the generation distance is the same for all common ancestors of a pair of individuals. Therefore, having worked out the relatedness between A and B due to any one of the ancestors, all you have to do in practice is to multiply by the number of ancestors. First cousins, for instance, have two common ancestors, and the generation distance via each one is 4. Therefore their relatedness is 2 ×(1/2)⁴ = 1/8. If A is B's great-grandchild, the generation distance is 3 and the number of common ‘ancestors’ is 1 (B himself), so the relatedness is 1 ×(1/2)³ = 1/8. Genetically speaking, your first cousin is equivalent to a great-grandchild. Similarly, you are just as likely to ‘take after’ your uncle (relatedness = 2 × (1/2)³ = 1/4) as after your grandfather (relatedness = 1 × (1/2)²= 1/4).”

          We can now see that parental care is just a special case of kin altruism. Genetically speaking, an adult should devote just as much care and attention to its orphaned baby brother as it does to one of its own children. Its relatedness to both infants is exactly the same, 1/2. In gene selection terms, a gene for big sister altruistic behaviour should have just as good a chance of spreading through the population as a gene for parental altruism. In practice, this is an over-simplification for various reasons which we shall come to later, and brotherly or sisterly care is nothing like so common in nature as parental care. But the point I am making here is that there is nothing special genetically speaking about the parent/child relationship as against the brother/sister relationship. The fact that parents actually hand on genes to children, but sisters do not hand on genes to each other is irrelevant,    since the sisters both receive identical replicas of the same genes from the same parents.”

         An animal may be pre-programmed in such a way that it behaves as if it had made a complicated calculation. This is not so difficult to imagine as it appears. When a man throws a ball high in the air and catches it again, he behaves as if he had solved a set of differential equations in predicting the trajectory of the ball. He may neither know nor care what a differential equation is, but this does not affect his skill with the ball. At some subconscious level, something functionally equivalent to the mathematical calculations is going on. Similarly, when a man takes a difficult decision, after weighing up all the pros and cons, and all the consequences of the decision that he can imagine, he is doing the functional equivalent of a large ‘weighted sum’ calculation, such as a computer might perform.

               If we were to program a computer to simulate a model survival machine making decisions about whether to behave altruistically, we should probably proceed roughly as follows. We should make a list of all the alternative things the animal might do. Then for each of these alternative behaviour patterns we program a weighted sum calculation. All the various benefits will have a plus sign; all the risks will have a minus sign; both benefits and risks will be weighted by being multiplied by the appropriate index of relatedness before being added up. For simplicity we can, to begin with, ignore other weightings, such as those for age and health. Since an individual's ‘relatedness’ with himself is 1 (i.e. he has 100 per cent of his own genes — obviously), risks and benefits to himself will not be devalued at all, but will be given their full weight in the calculation. The whole sum for any one of the alternative behaviour patterns will look like this: Net benefit of behaviour pattern = Benefit to self – Risk to self  + 1/2 Benefit to brother – 1/2 Risk to brother + 1/2 Benefit to other brother – 1/2 Risk to other brother + 1/8 Benefit to first cousin – 1/8 Risk to first cousin + 1/2 Benefit to child – 1/2 Risk to child + etc.

                The result of the sum will be a number called the net benefit score of that behaviour pattern. Next, the model animal computes the equivalent sum for each alternative behaviour pattern in his repertoire. Finally he chooses to perform the behaviour pattern which emerges with the largest net benefit. Even if all the scores come out negative, he should still choose the action with the highest one, the least of evils. Remember that any positive action involves consumption of energy and time, both of which could have been spent doing other things. If doing nothing emerges as the ‘behaviour’ with the highest net benefit score, the model animal will do nothing.

           Here is a very over-simplified example, this time expressed in the form of a subjective soliloquy rather than a computer simulation. I am an animal who has found a clump of eight mushrooms. After taking account of their nutritional value, and subtracting something for the slight risk that they might be poisonous, I estimate that they are worth +6 units each (the units are arbitrary pay-offs as in the previous chapter). The mushrooms are so big I could eat only three of them. Should I inform anybody else about my find, by giving a ‘food call’? Who is within earshot? Brother B (his relatedness to me is 1/2), cousin C (relatedness to me = 1/8), and D (no particular relation: his relatedness to me is some small number which can be treated as zero for practical purposes). The net benefit score to me if I keep quiet about my find will be +6 for each of the three mushrooms I eat, that is +18 in all. My net benefit score if I give the food call needs a bit of figuring. The eight mushrooms will be shared equally between the four of us. The pay-off “The pay-off to me from the two that I eat myself will be the full +6 units each, that is +12 in all. But I shall also get some pay-off when my brother and cousin eat their two mushrooms each, because of our shared genes. The actual score comes to (1 × 12) + (1/2 × 12) + (1/8 × 12) + (0 × 12) = +19 1/2. The corresponding net benefit for the selfish behaviour was +18: it is a close-run thing, but the verdict is clear. I should give the food call.

                 I have made the simplifying assumption that the individual animal works out what is best for his genes. What really happens is that the gene pool becomes filled with genes that influence bodies in such a way that they behave as if they had made such calculations.