# The Three Sexes Problem

Everyone knows that practically every species on Earth has reproductive sexes of male-female or none but what would happen if we had more than two sexes? Reliable Source on Worldbuilding asked a question to that effect. He laid out a fairly simple system where the three sexes were designated “A”, “B” and “C”. The As are the equivalent to Earth males in that they can get other people pregnant but can’t get pregnant themselves. Bs and Cs are similar to Earth females in that they can become pregnant but unlike Earth females, they can impregnate the other pregnable sex, i.e., a B can get a C pregnant but not another B. Reliable Source made no mention of what happens in homosexual pregnancies or if they are even possible, so they were ignored.

The sexes reproduce this way:

A+B=C

A+C=B

B+C=A

The dynamics of modeling such a system is beyond what Excel can easily do. I found a satisfactory modeling environment in AnyLogic Personal Learning Edition. It’s a Java based product with a broad range of capabilities. You can grab a copy on their downloads page. A copy of the project can be checked out from GitHub, if you’d like to follow along.

#### Model Construction

I started with a finite state machine that modeled the progression of birth, childhood, puberty (and attendant fertility), pregnancy, recovery, menopause and death.

There are several types of links in the diagram that represent the transitions between states. Let’s walk through them individually because they are the heart of the simulation.

Between Juvenile and Fertile, there’s a small clock that indicates a timeout. When an individual has been a Juvenile for 14 years, they hit puberty and become fertile. This transition to puberty at age 14 is true for As, Bs, and Cs.

Inside Fertile, there’s a link from Fertile to itself representing sexual propositions to other individuals. Since we want someone to stay fertile till they are impregnated, this link must stay within Fertile. Propositions are modeled as simple, single character messages expressing the sex of the individual who is propositioning for sex. Since we don’t care about lineage to answer our questions, just knowing who the other parent is sufficient. No family structures were modeled nor were members of this species given any kind of decorum in who they propositioned for sex. Any individual was equally likely to attempt to mate with any other fertile individual, regardless of whether that mating might result in a pregnancy or not. Very promiscuous compared to human standards but it was the easiest approach to take in the model.

The link between Fertile and Sterile is a conditional statement, asking if a [B|C] has had the maximum number of children OR if the individual has hit menopause (defined by a specific age) and can no longer have children.

The timeline between Fertility through Pregnancy and Recovery follows the normal human pattern of a 9 month gestation period followed by 1 year of recovery from the pregnancy. (I’m aware that physical recovery from pregnancy can be in as little as a few months but I chose a year to represent the contraceptive/libido crushing effect from breastfeeding and taking care of a newborn. This could easily be extended to 2 years in recovery.)

#### Model Environment

I chose an initial population of 20 with a data collection period of 100 years. With a new generation every 14 to 20 years, 100 years was sufficient to show any patterns that might emerge.

No attempts were made to account for any environmental or social factors that might dampen the underlying reproductive strategies. This was firstly simpler to perform in the model and secondly, the OP didn’t describe any possible dampening effects.

Not modeled:

• Infant mortality
• Variation in the number of pregnancies per individual
• Evolutionary fitness checks
• Effects of food supply on population
• Effects of trying to raise (or not) that many children.
• Any kind of social structure that has to do with breeding
• War or other death inducing conflicts
• Selection of ideal breeding partners by individuals

#### Discussion

This species is very sensitive to initial conditions. Seemingly small difference in the population’s sex ratios lead to wild fluctuations in ratios in two or three generations.

Overall population growth was exponential, as we would expect in a system where there are linear increases to the population.

Some sample runs for three groups, each with different initial population sex ratios. Note that the numbers provided are only for those individuals in the Fertile-Pregnant-Recovery cycle. Juveniles or Sterile individuals are not included in these counts.

• Initial population for Group 1: 10A, 6B, 4C leads to 602A 248B 234C at 100 years.
• Initial population for Group 2: 7A, 4B, 9C leads to 452A 447B 546C at 100 years.
• Initial population for Group 3: 8A, 7B, 5C leads to 548A 530B 454C at 100 years.

We can see that the initial population ratios were largely preserved though what these numbers don’t show is the fluctuations in population sex ratios prior to the 100 year mark.

Let’s have a look at Group 1:

Here’s Group 2:

Here’s Group 3:

#### Conclusion

We can see a huge performance improvement in population growth in groups that have a more balanced population sex ratio than one with an unbalanced ratio. Group 1has only about 3250 individuals after 100 years while Groups 2 and 3 were able to produce approximately 5000 individuals over 100 years. In a harsh environment with high infant mortality rates or struggle for resources, there will be huge social and sexual pressures to keep the population sex ratios as close to 1:1:1 as possible.

Warfare is equally brutal. Throughout human history raiding for females has been a common practice and this species will be no different, probably “worse”. If As are the equivalent to human males then an overproduction of As will lead to greatly increased chances for warfare/raiding between groups.

With more details about the environmental factors, the model could be extended to describe more complex interactions.

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