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 samegenes are identical by descent, and I think the answer to this puzzle lies in thinking hard about that concept. How
Table 13. Assuming
altruists use the rule,
Associate only with
relatives of degree r,
payoffs received by
individuals …
…playing …
Discriminating
Altruist
Selfish
Against individuals playing
Discriminating Selfish with
Altruist with
probability
probability p
(1 - p)
(p+(1-p)r)(b-c)
( p-pr)(b)
Total
Payoff
(1-p-(1-p)r)(-c)
Computations not
required; see
below
(1-p+pr)( 0)
Computations not
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
could you and your sibling share a gene NOT identical by descent? Well, let’s imagine that one of your parents had
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 .
selfish individuals meet altruists. Be definition such a decrease is equal to "s". But we
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 nonhymenopteran 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.