Paradox of Animal Sociality

Paradox of Animal Sociality,

Lecture #2002-13

"KIN SELECTION": ALTRUISM IN POCKETS OF RELATIVES.

In the previous lecture we laid out some general conditions for a kind of altruism to succeed, a form of altruism we called “discriminating”. We can tell a nearly well formed Darwinian Story about altruism coming to characterize the species if the population of the species is so organized that altruists find themselves in the company of fellow altruists more often than by chance and in the company of selfish individuals less often by chance and the sum of these two probability differences is greater than the ratio of the costs of the benefits to the altruist divided by the benefits given out by the altruist. The story would be of the form, "Altruists now exist in species X because in the history of that species, there were two kinds of organisms, altruists and selfish individuals, and altruists came to characterize the species because altruism was an inherited trait, and the population was organized such that altruists came into contact with altruists so much more often than by chance and selfish individuals came into contact with altruists so much less often by chance that altruists received the benefits of altruism to a greater extent than they paid its costs"

Given all the chest-beating that I have done over the last several weeks about a good model's specificity and the dangers of unintended surplus meaning, I would be remiss if I did not examine more precisely than I have so far, just which entailments of the word "discriminating" I intend and which I do not. It is tempting to think of discriminating altruism as "Be kind to individuals that are likely to be altruists: the more likely they are to be altruists, the more you should be kind." While this is a fair reading of the meaning of "discrimination" in ordinary language, it is a subtle misreading of the rule as we must understand it. The rule really should be thought of as, "Those of you who are among individuals likely to be altruists should be kind." In other words, discriminating altruism is discriminating only in a weird passive sense. It should not imply that altruists should seek out altruists to be kind to. Nor should it imply that altruists can even recognize one another. All it implies is that altruists that have been brought together by some circumstance unrelated to altruism should be kind to one another.

Altruism in Pockets of Relatives

In this lecture we explore the rule, "Those of you who are among relatives of a certain degree, should be kind" to see if it is a form of discriminating altruism in our limited passive sense of "discrimination". It answers the question, "If some force in nature were to bring together relatives of a certain degree, and if some of those relatives were to have a trait for altruism, would altruism spread in the population?" We can answer the question if we can connect the concept of relatedness with the concept of discrimination in the limited sense we have here defined it. In the last lecture, we used a games table to define discriminating altruism, invoking two variables: a, the increase in the probability of altruists meeting altruists, and s, the decrease in the probability of selfish individuals meeting altruists. We demonstrated that if the sum of a and s exceeded the cost/benefit ratio, then altruism would evolve. If we could connect the concept of relatedness with "a" and "s", we would have connected relatedness to discriminating altruism.

To make this connection, we might ask ourselves the following question: "If I were an altruist and I learned that the person standing beside me was a long lost Relative of degree r, a long-lost brother (r=. 5, cousin (r=. 25), or identical twin (r=1.00), what would I have learned about the probability that that person was an altruist?" To answer THIS question, we need to know what it means to say that somebody is a degree r relative of yours. The term "r" (=relatedness) refers to the probability of your sharing a gene with a relative by descent. (IBD). . We share a gene by descent if one of us gave to the other or if some ancestor gave it to both of us. So, to say that your brother is a degree 0.50 relative of yours is to say that, for any particular gene, you and your brother have a 50-50 chance of having both received that gene from your parents. The analysis that produces this conclusion is called "path analysis". It starts with designating a particular relative, A, and traces all the paths by which the same gene might have been passed to relative, B. Two individuals are related (IBD) if they can be connected by such paths and the degree of their relationship is proportional to the number and length of such paths.

For instance, what is the chance that you have any particular gene, I.B.D. from your mother? Well, for any animal that has two parents, such as yourself, the chance that it came from your mother is exactly one half. (The other half is the chance it came from your father, right?) So, the degree of relatedness between yourself and your mother is 1/2. The same reasoning applies to your father: you are 1/2 related to him because there is a 50-50 chance that any one of your genes came from him.

How related are you to your sibling. Well assuming that you have the same father, the answer is 1/2. Why? Well, we have already established that given that you have a particular gene, there is a 50 percent chance that you got it from your mother. You won't share this gene via your mother, unless she also gives it to your sibling, which she will half the time. (The other half of the time, she will give the gene on the other chromosome, the one that does NOT contain the gene you got.) So the total probability that you will share a gene via your mother is (the probability you got it from her) times (the probability she gave it to your sibling) or (1/2 x 1/2) or 1/4. Why "times"? Because the probability of both of two events occurring is the product of the probability of either of them happening. Since the same reasoning applies to the probability that you will share the gene via your father, that probability is also 1/4. The probability that you share a gene by EITHER parent is the sum of the probabilities that you share a gene by each and so 1/4 + 1/4 = 1/2. Why SUM in this case? Because the probability of two independent events occurring is the sum of the probabilities of EITHER of them occurring.

What happens to the relatedness of siblings when they are the children of DIFFERENT fathers? Well, the probability of sharing a gene via the mother remains the same, 1/4. The chance that any particular gene in you was obtained from your father remains 1/2, but the chance that your father gave the gene to your half-sibling is now zero because YOUR father gave no genes to that sibling at all. So the total probability of sharing a gene via your parents with a half sib is just 1/4. And, unless your two fathers were brothers or some other degree of relative, 1/4 is the r between you and your half-sib.

Notice that stating the probability of sharing a gene I.B.D. is not the same as stating the total probability of sharing a gene. Sharing IBD is not the only way that you can share a gene. You share many genes with the mice that live in Jonas Clark Hall and presumably none of these mice are relatives. You share these genes because every mammal has them. Consider, for instance, the gene for hemoglobin. No matter who the other person is, no matter how unrelated they are to you, the probability of your sharing that gene is 1.00 I know this because I know that the gene for hemoglobin is fixed in the human population, and there is no other gene in the human population for you to share. The probability of any person's having that gene, given that person is human, is 1.00.

Now, of course, not all genes are fixed. One obvious example is the genes that govern hair color or eye color or ear shape. Sitting on the bus looking at strangers you may notice that a stranger has the same eye color as your brother or the same ear shape or even both. But this does not mean that you have necessarily discovered a long-lost relative. Why? Imagine, for an example, that half the population carries a gene for a "disconnected" earlobe. If your brother has a disconnected earlobe, there is a 50-50 chance that the stranger will have a disconnected earlobe even if he is not a relative. So even in the absence of information about common ancestry, you have chance of your sharing a gene and that chance is equal to the proportion of individuals in the population bearing that gene. The information that the stranger on the bus is a relative provides an INCREASE in that probability.

So I hope by now you are beginning to see how relatedness relates to discriminating altruism. Given that only relatives of degree r are available to interact with, there are two ways in which the individual an altruist is interacting with can come to be an altruist: (1) Because that individual is an altruist BY CHANCEi and (2) because that individual shares the altruistic gene ibd. An individual will always encounter at least p altruists by chance, no matter how closely related are the other members of the population. So, the chance that a relative of an altruist is another altruist is always p + (?). The balance (the + ?) must be some portion of the (1-p) remaining individuals, that portion that share a gene ibd. Since these are all relatives of degree r, the probability of sharing a gene with any one of these is r, and the number of individuals that will share the altruist gene with an altruist is therefore r(1-p). Thus, the total probability of altruist gene sharing is p + r(1-p). The analogous logic gives the probability that an altruist will associate with a selfish individual as 1-p+pr. (The chance that a relative of an selfish individual is another altruist is always (1-p) + (?). The balance (the + ?) must be some portion of the (p) remaining individuals, that portion that share a gene ibd. Since these are all relatives of degree r, the probability of sharing a gene with any one of these is r, and the number of individuals that will share the altruist gene with an altruist is therefore (1-p+ pr)." Hence (by subtraction) the probability that an A individual will pair with an S individual as p-pr.

For those of you who, like me, are algebraically challenged, this may be a lot to swallow. Often it helps in understanding a mathematical expression to take it to the extreme. If the expression makes sense in the extreme, then it is easier to imagine that it makes sense in all the intermediate cases. Take the idea that given that only relatives are present to interact with, altruists meet altruists p + (1-p)r of the time. Lets imagine that each of us had only an identical twin to interact with. Since identical twins are 100% related, the value of P + (1-p)r becomes p + (1-p)(1)) or simply 1. In that case, each altruist MUST meet another altruist. That makes sense, doesn’t it? How about when the "relative" isn’t related at all, r = 0. In that case (p + (1-p)r) becomes p. In other words, if the "relatives" aint related, then the probability of meeting an altruist is just the probability of meeting one by chance.1

1 “How can one receive a gene by chance?” or “How can one receive a gene other than by descent.” Oddly enough the two ideas, by chance and by descent, appear to work just fine by themselves, but conflict when we bring them together. There is no problem in asking the question what is the probability that, given that one person has a gene, that another person chosen at random will have the SAME gene. The answer is p, the relative frequency of the gene within the population. Further more, there is no problem in answering the question of what is the probability that two related individuals will share a gene IBD. That is the procedure laid out in the previous class. There is even no problem with saying that the first number will be lower than the second number, since relatives presumably share genes more often than individuals chosen at random.

But a problem does seem to arise when we put these two ideas together, because, as the alert reader may point out, all genes are received “by descent”. Furthermore, any two genes that are the same gene are identical. But, not all same- genes are identical by descent, and I think the answer to this puzzle lies in thinking hard about that concept. How could you and your sibling share a gene NOT identical by descent? Well, let’s imagine that one of your parents had Table 13. Assuming Against individuals playing altruists use the rule, Discriminating Selfish with Associate only with Total relatives of degree r, Altruist with probability payoffs received by probability p (1 - p) Payoff individuals … …

Computations not … (p+(1-p)r)(b-c) (1-p -(1-p )r)(-c) required; see p Discriminating

l below a Altruist y i n Computations not g Selfish ( p-pr)(b) (1-p+pr)( 0) required: see below Since + (1-p)r is an INcrease in the frequency with which altruists meet other altruists (i.e., an "a"), and -pr) is a DEcrease in the frequency with which altruists meet selfish individuals (i.e., an "s"), and since WE ALREADY KNOW THAT a + s > c/b, then altruists will increase in the population when (1-p)r+pr>c/b or when r>c/b. Familiar?

But look carefully at the two expressions, p + (1-p)r and p -pr. The first shows an INCREASE in the frequency with which altruists meet altruists. By definition such an increase is equal to "a" The second shows a DECREASE in the frequency with which selfish individuals meet altruists. Be definition such a decrease is equal to "s". But we two copies of the gene in question. That parent gave you one copy but gave your sister the other copy. Both you and your sister share a gene, but not identical by descent.

How often would siblings share a gene NOT identical by descent? Both of two things would have to happen. First, it has to be true that the gene is in your sister because the parent gave the gene it gave to you to the sibling. Since we know that the probability of sharing a gene IBD is r, the probability of NOT sharing it IBD is (1-r). If the parent did not give the gene that it gave to you to your sibling, then she or he MUST have given your sister the OTHER gene, whatever that was. What is the probability that that other gene is the same kind of gene? Well, it is the probability that any gene in the population is that kind of gene: p, the relative frequency of that gene in the population.

SO…, the total probability one related individual will share a particular gene of his relative is the sum of P{share by descent} + P{share by non descent}. When we say share by non-descent here we do NOT mean that the sibling did not receive the gene from his parent. What we mean is that the sharing was not achieved via a continuous pathway of genetic copying from one sibling through the parent to the other sibling. The parent gave the gene to your sister, but that gene, even though it was identical to the gene it gave you, was NOT copied from the same gene as the gene given from you. It was copied from the other one, which happened by chance to be the same. Here is the origin of the words, “identical by chance.”

What is the sum of the two probabilities? We know that P {share be descent} is “r”. That is what we figured out by path analysis. And we know that P{share by non-descent} is (1-r)p, because we JUST figured that out. So, the sum of the two probabilities is, r + (1-r)p .

Now, this can be re-arranged in a more familiar form: p + (1-p)r . already know that discriminatiing altruism can come to characterize the species if a+s>c/b. So, by substitution, we know that altruism can come to characterize the species if p + (1-p)r + pr > c/b or, simply, r > c/b

This inequality might be familiar to you. It might be more familiar if it re-written as rb>c. It is Hamilton's inequality, after William Hamilton, its inventor. Hamilton introduced the idea in 1964 in a paper that started the whole sociobiological revolution and launched the careers of many of the people you are reading about in your textbook. Of course one of those careers was that of Richard Dawkins.

Kin Selection Theory

I have presented you as best I can the mathematical basis of kin selection theory. You should be aware, by now, that it is a theory about what sort of behavior organisms should display toward one another when circumstances compel them to live side by side with relatives. But as you know from reading Dawkins, kin selection theory is often presented in a very different way. It is not presented as a story about what happens in a population organized into pockets of relatives; rather it is told as a story about helping relatives as a dilute form of reproduction. This view of kin selection theory we owe to William Hamilton.

Hamilton looked at the problem from the point of view of the altruist. He regarded altruism toward relatives as an inefficient way of producing oneself. After all, in reproducing children, one only creates individuals with half one’s genes, on the average. That’s only twice as good as making first cousins or 4 times as good as making second cousins. If the benefits of helping brothers to make first cousins were more than double the costs in helping oneself to make children, then shouldn’t the trait “helping brothers” make more of itself (by helping brothers) than the trait helping oneself makes of itself (by helping oneself)? Hamilton thought so.

The model is very simple. He said, “Imagine a population in which every individual has exactly one relative of degree “r” to interact with. Let r = the degree of relationship between the potential altruist and the potential beneficiary. Let c = the costs the altruists incurs in helping and let b = the benefits enjoyed by the beneficiary. Let’s give the reproductive output of helping oneself a value of 1. Then 1< r(b/c) for altruism to be selected. That is altruism between relatives of a given r will only occur if the benefits of that altruism so exceed the costs that reproducing through relatives produces gene copies than reproducing for oneself.

What made Hamilton's theory an instant success was that it permits very specific predictions about the relationship between the consanguinity of any two neighbors and the probability of seen altruism between them. The classic demonstration of the usefulness of this principle is the behavior of honeybees. The extreme altruism of worker honeybees had long been a puzzle for Darwinian theory. You will recall from your television specials that a honeybee colony consists of workers who are all sisters working toward the reproduction of their mother. The worker bees perform elaborate feats of coordinated labor, gathering building and food materials, concentrating those food materials into storable form, cooling and warming the hive, helping the queen lay her eggs, and caring for the young as they develop. The odd feature of the colonies from a Darwinian point of view is that, of the tens of thousands of individuals in the colony, only a few are capable of reproducing. . The rest, the workers, are sterile individuals that simply work toward the reproduction of the queen and the dissemination of her of her non-sterile offspring. How could their sterility ever have been selected for?

The non-sterile offspring of the queen are of two kinds. Drones are males raised by the workers that have no function but to fly from the hive in search of mates. Reproductive females, called queens are raised by the workers on a special protein rich food source. They are larger than the workers. When they emerge from the cell in which they developed, they fly from the hive on a nuptial flight. During this flight they are found and mated by one or more drones usually from a different hive.

The colony reproduces by budding. Either the original queen or one of the virgin queens departs the hive with a group of thousands of workers called a swarm. Carrying several days supply of food with them, the swarm takes u a temporary perch on a tree branch and the workers scout for a new hive site.

Now the most obvious puzzle has to do with the behavior of the workers. But once you know that the workers are the sisters of the queens, then perhaps you can imagine that working in the service of sisters makes in the long run for more honeybees (who work in the service of sisters) than working in the service of self makes honeybees (who work in the service of self). What was so exciting to people, however was how it explained the distribution of such altruism among insects. You see, a great many insects display altruism such as that displayed by honeybees. But all of them are hymenopterans – bees and wasps. Social systems of that degree of altruism are not observed among non- hymenopteran insects. (with one exception, the termites, which are a special case). So what is so special about the hymenopterans?

What is special about them is their sex determination system. As we observed above, among most of the animals we are familiar with – including ourselves – maleness is determined by the possession of a special chromosome called the Y chromosome. Males have one, females don’t. In hymenopterans, the males have only one set of chromosomes, whereas the females have two. As the queen is laying eggs she decides whether to make a female or a make offspring as follows: In one special pouch she keeps her eggs and in another special pouch she keeps the sperm that she got from the male or males she mated with. If she wants to make a female offspring (including workers) she allows sperm to reach the egg. The egg is thus fertilized and the resulting offspring has two sets of chromosomes. If she wants to make a male, then she passes an unfertilized egg into the cell. The resulting offspring has only one set of chromosomes and is thus a male.

Now to the extent that queens mate with only one drone (a point in contention) then all the females in the hive have the same father. Since he can only give one set of chromosomes to his offspring (he only has one to give, right?), then all the females in the hive have that one chromosome. So if, for instance, a haploid father has an altruist gene, then his daughters MUST also have that gene. The long and the short of it is that sisters are ¾ related in hymenopterans whereas mothers are only ½ related to their daughters. Consequently, it is more probable, from the point of view of kin selection theory, for a sister to help a sister make nieces than it is for a mother to help a daughter make grandchildren. Thus, the existence of females helping sisters reproduce is expected among hymenopterans where it is not expected breeding systems similar to our own.

Hamilton’s theory explained why most of the extremely social insect systems were among hymenopterans. The prevalence of eusociality among bees and wasps had long been a puzzle to socio-biologists, so Hamilton explanation was treated as a great triumph. It was because of this argument, more than any other, that Hamilton's theory became immediately and widely accepted. Other triumphs have been claimed for kin selection theory. Using kin selection theory, theorists have frequently predicted that where animals live in groups of mixed parentage, as monkeys or prairie dogs or humans, for that matter, that altruistic behaviors should be directed selectively toward relatives. So prairie dogs should be expected to give alarm calls more when relatives are in danger, and monkeys should be expected to groom relatives more than non-relatives and, in human social systems where parentage of males offspring is in doubt (the females are promiscuous) uncles should take more care of their nephews and nieces than of the children of their wives. All these phenomena have been observed.

Proponents of kin selection theory may have claimed too much. In the first place, hymenopteran females are not monogamous. In fact, honeybee females, the very subjects on which kin selection theory is based, mate multiple times. Each additional mating decreases the probability of sharing a gene IBD among the female offspring. If the female mates with two males, the offspring are related by 1/2, just like you and your brother. If the female mates with three males, the offspring are related by 5/12, 4 males 3/8ths and so forth. In fact, the only condition under which hymenopterans should be expected to be more eusocial than mammals is when the females mate with only one male, a condition that is not commonly observed.

In the second place, the extension of the theory to creatures like prairie dogs that live in mixed colonies of relatives and non-relatives may be more than kin selection can do. The "discriminating altruist" of the prairie dog theory is like a diner who attends only the best restaurants or picks out the best foods on the menu. But remember that the discriminating altruist of kin selection theory is like a discriminating diner who eats well only because he has never been brought to a restaurant where bad food is served. Thus, the theory invokes discrimination only in the sense that it requires that only relatives of degree r interact, but it provides no mechanism for bringing relatives together. That mechanism (which, after all provides the "discrimination") must come from outside the theory. Now we can think of many such mechanisms. For instance, when baby birds are born into a nest together, they must, of necessity, be siblings, i.e., individuals related to each other by one half (or at LEAST one quarter if they do not share a father.) Another example would be insects from eggs all laid by the same mother on the same leaf of a tree, which, similarly, must be related to one another. Thus, before we can believe the kin selection version of discriminating altruism even in the weak passive sense of the model I have presented to you, we have to have another theory that tells us why relatives of a particular degree -- and only those relatives -- come to be close to one another. . Prairie dogs, who are raised in burrows that spread out over the landscape if the animals thrive, may be distributed in groups of relatives. But the behavior reported of prairie dogs -- that they preferentially give alarm cries in the presence of relatives -- seems to suggest the evolution of discrimination in a more active sense.

Conclusion.

The goal of this chapter has been to show that Hamilton’s kin selection theory is actually a verson of discriminating altruism as outlined in the previous chapter. It shows that Hamilton’s Kin Selection theory works because when kin interact with kin, either because they choose kin or have no other choice but to interact with kin, they alter the probability of similar organisms meeting one another. And it is this biasing of the probability of kin meeting kin (and non kin meeting non kin) that drives kin selection, not the fact of their kinship itself. In the following chapters, we will explore other methods by which the meeting of altruists with altruists might be biased. i