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THE EVOLUTION OF THE 50/50 SEX RATIO:
A COMPUTER TUTORIAL AND SIMULATION OF AN EVOLUTIONARY STABLE STRATEGY


Michael E. Mills, Ph.D.
Psychology Department
Loyola Marymount University
Los Angeles, CA 90045


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Copyright 1991 Michael E. Mills


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We often hear the phrase that evolution occurs for the "good of the species."
However, as we will see in this tutorial and computer
simulation, this is a "specious" argument.  (sorry... )

Since goal in the "game of life" is leave as many offspring as possible, if
evolution occurred for the "good of the species" we would expect
various species to compete with one another to maximize their relative
numbers.  The species with the greatest population would "win."

We would also expect that individual members of a species would sacrifice
their own personal reproductive interests for the greater reproductive
interests of the species.  Once the population of the species had reached 
the "carrying capacity" of the environment (e.g., just enough food 
available to support everyone), we would expect this speciesto reduce 
its reproductive output.   
Note that this goal is in direct conflict to the interest of individuals who 
wish to maximize their own reproductive output vis-a-vis the reproductive
output of other individuals.   So we have a situation wherein the goal
of the "good of the individual" is in direct conflict with the goal of
the "good of the species."   Which wins out?  Do individuals behave
cooperatively for the good of the species, or do they behave selfishly and
continue to reproduce to maximize their own personal reproductive output
(even at the peril of the reproductive output, and possibly even the
survival, of their own species)? 

Before we answer that question, let's also look at another phenomenon
wherein the interests of the species conflict with the interests of
the individual: the sex ratio.    Before the carrying capacity of the
environment is reached, we would expect that a specieswould attempt
to increase its population as quickly as possible.  In that way, it
will win out in the competition with other species.  Since the number of females
is the limiting factor in determining the reproductive output of the
species, to maximize its reproductive output we would expect species
to evolve a sex ratio of about 95% females to 5% males.   Compared
to a 50/50 sex ratio, this 95/5 ratio will almost double the
reproductive output of the species.  

But why does the 95/5 sex ratio conflict with the reproductive interests 
of an individual?   Wouldn't it also be in the interests of an individual
to have mostly daughters, in that females usually have no problem finding
males who are willing to copulate with them?  Also, males have a higher
mortality rate, and a few males will have difficulty finding any 
female who is willing to copulate with them.  
Daughters, it seems, would represent a
more of a "sure bet" -- less of a gamble than sons.   

However, in a population composed of 95% females, having a son
would definitely be in individual's reproductive interests.
Unlike a female, a male's reproductive output is not limited to his
own biology.  Rather, it is limited only by the number of different females
to which he can get sexual access.   Since there are 95 females for
every 5 males in this population,  a son could have many times the
number of offspring that a daughter could have.   

If the sex ratio
pendulum should swing far to the other side, so that the sex ratio
is now 95% males and 5% females, you can see that having a
daughter would now be in your personal reproductive interests.    
There will be a lot of sons who are completely "reproductively
disenfranchized" -- unable to find a female.  

So, what is the best strategy to follow if you wish to maximize your
own personal reproductive interests?   What proportion of sons vs.
daughters would you like to have?  It turns out that the overall
best strategy is to have about 50% daughters and 50% sons.  This
is called an "evolutionary stable strategy," or ESS.  An ESS is
a strategy that in the long run, on average, cannot be bettered by
an alternate strategy.

Thus, we have a dilemma:  the reproductive interests of the specie
(95/5 sex ratio) is at odds with the reproductive interests of the 
individual (50/50 sex ratio). 
As an individual, will you attempt to work for the "good of the species" 
by having 95% daughters and 5% sons, or will you attempt to maximize
your own personal reproductive output by having 50% daughters and 50% sons?

It appears that selection virtually always occurs at the 
level of the individual,
not the species.  Individuals often will continue to have offspring
even after the carrying capacity of the environment is exceeded, often resulting
in a mass starvation.   The sex ratio for the vast majority of species
is about 50/50.  

Right now, let's create our own miniature universe: a computer
simulation.  We will set up
the rules, and then see what evolves in our computer simulated little universe.
We will see what happens to a hypothetical population that
initially consists of 80% males and 20% females.  Will the resulting
sex ratio be 95% females and 5% males, or will it work out to an
evolutionary equilibrium point of the 50/50 sex ratio?  Let's see.

Here are the rules:

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1.  Males and females are free to move about in any direction.
Males and females not of reproductive age are grey.  Reproductive
males are blue, reproductive females are red.

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2.  When a reproductive male and reproductive female encounter
one another, they spend a second or two courting.  If they like
each other (there is an 80% chance that they will), 
they mate.  Mating is indicated by the pair blinking on
the screen and the sound of a beep on the computer speaker.

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3.  For each mated pair, there is a 70%  chance that they will have
one offspring, a 20% chance that they will have two offspring, and
a 10% chance that they will have three offspring.  Offspring are
placed as close to the parents as possible, in the first available
empty space.  Offspring do not become reproductive for a few seconds,
and until they become reproductive they are grey.

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4.  After mating, the pair splits apart and goes off looking for
another mating opportunity.  That is, they are "serial monogamists."
However, after mating, there is a few second delay before they
are allowed to mate again.  

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5. Individuals die after about 10 seconds of life.  Their death is
indicated by their disappearance from the screen.

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6. We will start off with 200 males and 50 females. 

Press the ESC key to begin.
