Demographic Impacts of “The Very Special Spell”

Because I am a giant nerd with an MBA, for fun I built a simple spreadsheet model of the demographic impact of the “Very Special Spell” in Estee’s Triptych Continuum. This spell allows two mares to bear a foal, but all these foals are fillies. This spell is used to explain the population dynamics in the Triptych Continuum.

My model's inputs are:

• The starting Male/Female population percentages (50%/50%) 
• The number of foals born to each grouping of ponies (fertility rate)
• The social bias connected with Male/Female groupings as opposed to other types
• The percentage of groupings that are polyamerious. 

The outputs are:

• Male / Female population percentage each generation
• The population percentage of each type of grouping each generation (M/M, M/F, F/F, M/M/M, M/M/F, M/F/F, and F/F/F)

Notes

• I ran the simulation for 20 generations and looked for the values to stabilize.
• I used Male and Female in the model instead of Stallion and Mare because I found it easier to remember the initials M/F rather than S/M.
• I’m a guy and put M before F when I built the model. Likely this was unconscious bias.

Assumptions:

There is potentially a social bias associated with Male/Female (M/F) relationships vs. other types of groupings (M/F Bias in the model).

• 100% = No social bias or special weighting. Ponies are as likely to choose any partner, regardless of gender.
• 200% = Social bias in favor of M/F relationships. Ponies are twice as likely to pick a M/F relationship as the baseline chance.
• The weighting for each type of relationship can be adjusted individually in the hidden “Social Bias” section.

There is potentially a social bias associated with polyamerious relationships.

• This is represented by a weighting % of all relationships that are polyamerious (Poly% in the model).
• For simplicity, all Poly relationships are represented by threesomes (M/M/M, M/M/F, M/F/F, F/F/F).

Other than these biases, ponies are otherwise equally likely to choose partners of either gender.

All groupings that can bear foals are assumed to have an equal number of foals each generation.

• F/F or F/F/F groupings can only bear Female foals with the “Very Special Spell”.
• M/M and M/M/M groupings can not bear foals. They can adopt, but this is assumed to be represented by a foal that was birthed by another group. 
• M/F/F groupings are more likely to bear Female foals (33% Male / 67% Female) because depending on which ponies come together, sometimes they use the “Very Special Spell” and sometimes they don't need to.
• The fertility of each relationship type defaults to 200% and can be adjusted individually in the hidden Foals/Group section).

Highlights

Without “The Very Special Spell”, if the M/F population split starts at 50%/50%, then it stays at 50%/50% regardless of the other input variables.

With “The Very Special Spell” the results depend on the inputs.

If the M/F Bias is set to 100%, with no special weighting for M/F groupings over any other kind, then the Male population goes into rapid decline (50%, 33%, 25%, 20%...). After 20 generations the Male % is less than 5%. 

Increasing the M/F Bias to 125% stabilizes the situation, with the Male % dropping less than 0.1% per generation in the 20th generation. With a Poly % of 0%, in the 20th generation Females and F/F groupings dominate the demographics:

19% Male
81% Female
3% M/M
33% M/F
65% F/F

In trying to replicate the cartoon, I tried a M/F Bias of 165% and a Poly % of 0% (I don’t know of any polyamerious groupings in canon). By the 20th generation, the results stabilize at:

33% Male
67% Female
6% M/M
53% M/F
41% F/F

This has Mares outnumbering Stallions by 2 to 1 and M/F groupings only outnumber F/F groupings by about 5 to 4.

The head canon for my stories is represented by something like a M/F Bias of 155% and a Poly % of 10%. In the 20th generation, the results stabilize at:

29% Male
71% Female
5% M/M
44% M/F
42% F/F
>1% M/M/M
1% M/M/F
4% M/F/F
4% F/F/F

This has Mares outnumbering Stallions by about 2.4 to 1, F/F groupings about as likely as M/F ones, and Poly groupings that are uncommon but not unusual and mostly dominated by Mares.

What kind of population dynamics does your head canon envision?

Note, in the comments, CCC pointed out an error in how I was calculating the Male / Female percentages. I fixed the model, adjusted the parameters, and revised the results in the post above. Thanks CCC!

Comments

[Jordanis]

I have been wanting to see a basic analysis like this for so long that it's shocking I never figured out how to do it myself.

Of the results you posted, your headcanon is the one that most closely resembles what's been in my head.

[one of the herd]

huh, shame i cant upvote a blog. i love looking at the numbers for stuff like this.

What kind of population dynamics does your head canon envision?

my personal head canon would put the m/f bias at somewhere around 200% (i dont imagine a actual gender bias but i could see nearly the same effect resulting from the difference in planned pregnancies taking the time to involve a spell and accidental pregnancies from nature taking its course... maybe a better metric would be to set the birthrate of m/f pairings at 200 to 250% but leave the gender bias flat?) but i would put the poly bias around 95%. (i like to imagine that the monogamous relationships we see in the show are the exception and we only see them cause they stand out) no idea what that would do the the end result though

[CCC]

If the M/F Bias is set to 100%, with no special weighting for M/F groupings over any other kind, then the Male population goes into rapid decline (50%, 33%, 25%, 20%...).

Fun fact - it's possible the show that, at the start of Generation X, 1/(X+1) of the population will be male.

At the start of Generation 1, 1/2 is male.
At the start of Generation 2, 1/3 is male.
At the start of Generation 3, 1/4 is male.
At the start of Generation 4, 1/5 is male.

And so on. So, by Generation 20, 1/21 will be male - a little less than 5%. Of course, by then a lot of the females interested in males will simply not be able to find a partner, and will compete aggressively for the few males that are there...

...but I get the impression that the Most Special Spell hasn't been around for twenty generations yet, in Estee's works. Three, maybe four generations tops - so there would still be at least a 20% male population.

17% Male
83% Female
3% M/M
33% M/F
65% F/F

....something's wrong here.

33% M/F and 3% M/M requires that at least 19.5% of the population be male. But only 17% of the population is? What's going on here?

[bigbear]

5557652
You were right! I was using the wrong numbers in my Male and Female percentages. I fixed the model, adjusted the parameters, and revised the results in the post above. Thanks CCC!

5557574
I ran the revised model with your suggested 200% M/F bias and 95% Poly %. After 20 generations, the % of Stallions is still dropping very slowly, and F/F/F are very much the dominant type of grouping.

10% Male
90% Female
>1% M/M
2% M/F
4% F/F
>1% M/M/M
3% M/M/F
23% M/F/F
69% F/F/F

[one of the herd]

5558478
assuming cultural norms shifted with the changing population just enough to stabilize around there, that would match my own personal head canon quite well actually. cool.