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What we're interest in, is the altruistic corner of Hamilton's universe - which we discussed
in another presentation. So how can it be, that we can sacrifice to
benefit others, and in doing so diminish our reproductive success and enhance theirs?
It would appear that doing that, would be a good way to go extinct.
This was a puzzle that Darwin was aware of. It was one of several statements that he made
about what would falsify his theory centered on natural selection.
So in chapter eight of the Origin of Species, Darwin notes:
this was ants who seem to assist their siblings, rather than reproducing themselves, they assisted
their siblings in reproduction, and were sterile. And the question was: how could they evolve?
Darwin suggested it would have to do with family. That they were close family.
And this later became the core of Hamilton's Rule.
So Hamilton, W.D. Hamilton, was a young graduate student in the 1960s when he came up with
this. And his solution was that such altruism could
evolve when rB>C. So what we have to do to understand this inequality,
is first define our terms. Remember, that our interest is in reproduction.
So we're talking about reproductive costs and benefits.
The B ... refers to the reproductive benefit, to the recipient, of the altruistic act.
So B stands for benefit, and the benefit is the benefit in greater reproductive success
that's enjoyed by the person that the altruist assists.
The C refers to the reproductive cost to the altruistic donor.
So B is simply a benefit, and C is a cost. This is just a kind of cost-benefit analysis.
In this case, the benefit goes to the recipient of the altruistic act.
And the cost is borne by the altruistic donor. And these are reproductive costs and benefits.
So what's going on here, in altruism, is that the actor being benefited, has more reproductive
success as a result of that, and the one who benefits them, has diminished success.
And this would seem to predict that the altruistic line would go out, would cease to exist.
Because it's not benefiting itself, it's benefiting others.
This brings us to the last term, the r. And this simply has to do with how closely
related the altruist and the recipient are. So this, technically, refers to the coefficient
of relatedness. There are different measures of relatedness.
There's quite a bit of discussion and controversy about how to best measure this.
But we're going to use a very simple calculation. So we can rewrite that inequality, move everything
apart from the zero, so that Hamilton's Rule is rB-C > 0.
So relatedness is taken and multiplied against the benefit. We then subtract the cost.
And as long as the result of that is greater than zero, altruism is possible.
So our first step is ...
Our second step then is to subtract the cost. We're gonna use a really simple example.
to illustrate this. By the simplest calculation your daughter
has a 50% chance of sharing a new gene, which might be a new gene for altruism.
And an important point here, we discussed earlier in the class, is that 99.9% of the
human genome is invariant. We're not interested in that 99.9% here.
What we're interested in is how a new gene, that would influence you to behave altruistically,
could ever evolve? So that's why we do this math in this way.
An offspring is a 50 percenter, they get half their genome from you, and half from their
other parent. So that means they have a 50 percent chance
of getting your gene. Your sister is also a 50 percenter, if you
share the same parent, and so full siblings are 50 percenters.
The daughter of your sister, your niece, is a 25 percenter.
And to calculate this, as we step out from you, we simply multiply by 0.5.
And it basically cuts the likelihood in half, at each step away from you.
So the outcome of this way of thinking is that two nieces are equivalent to one daughter.
In terms of the likelihood of a given gene surviving.
And that my be an altruistic gene. This means that three nieces are greater than
one daughter. So let's say that I have a new gene, that
causes me to behave altruistically, if I sacrifice, and it leads to the survival of three nieces,
who also share that gene, I've done better than if I produced the one daughter.
Or I have a greater likelihood, by helping three nieces survive, in assisting that gene
to be around. than if I simply help one daughter survive.
So here's the math on this In the case of nieces (or nephews, or a niece
and two nephews, it doesn't matter) the benefit is .25, and I helped three nieces
to survive, so we multiply the .25 times three. The cost was .5, I did not have a daughter
as a result. of all of my efforts to help my nieces.
So we multiply that by one. The result of that is we get ...
So that means that that gene, can have greater likelihood of surviving through my altruistic
actions if I forgo my own reproduction and assist
others in reproducing, I can help that altruistic gene to survive.
As long as I'm helping close relatives, and as long as the likelihood of the gene
surviving in my close relatives is higher than it would be in terms of my direct offspring.
So from this, we can draw this lesson. You can benefit more from helping a sibling raise
nieces or nephews than by raising one daughter (or son) of your own.
I've kept the gender, just focused on the female line here to simplify things.
So the bigger rule here, the bigger insight, is that genetic interests are greater than
our direct offspring. They can also include nieces, they can also
include cousins. They can include obviously nephews.
And this is called inclusive fitness. So, your direct reproductive fitness refers
to how many offspring, you have, who survive to reproduce themselves.
Inclusive fitness goes beyond your direct offspring, to also include your close relatives
who survive to reproduce themselves. And Hamilton's Rule suggested that the key to understanding
reproductive success was inclusive fitness, rather than direct fitness.
This came to be called 'kin selection' after an essay by John Maynard Smith. And it's simply
the idea that social cooperation - societies - can evolve through close kin assisting one
another. This was one of the key launching points for
sociobiology. This means that altruism among kin, or the basic argument here is that altruism
among close relatives is actually genetic self-interest, and so this squares with the
idea of survival of the fittest through natural selection. But your fitness can be increased
through altruistic action, when you're helping those who are closely related to you,
to also reproduce. Based on this we can draw a prediction. And
the basic prediction of Hamilton's Rule, is that relatedness - actual genetic relatedness
- to social life, and the emergence of societies in animals. And this should include humans,
by the Darwinian logic that humans are also animals, and the same principles that we can
use to explain social life across life as a whole, we can apply to humans.