Animal Crossing: New Horizons - Flower Breeder

Compute probabilities for flower parent and offspring genotypes in Animal Crossing: New Horizons.

Prerequisites

Written in python v3.7.0

Getting Started

Flower genotypes and phenotypes are pulled from the table on the Animal Crossing Wiki Article on Flower Mechanics.

Generic seed flower objects are predefined with names "Seed", e.g. RoseSeedWhite.

Single offspring probabilities are evaluated by multiplying two parents together

>>> a0 = RoseSeedWhite * RoseSeedWhite
>>> print(a0)
BayesObj{
  (R:gg)(Y:gg)(W:GG)(B:gg)[Color.PURPLE]:1/4
  (R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]:1/2
  (R:gg)(Y:gg)(W:gg)(B:gg)[Color.WHITE]:1/4
 }

Offspring can be selected based on color by using the Pick() option with the lambda generator PickColor()

>>> a1 = a0.Pick(PickColor(Color.PURPLE))
>>> print(a1)
BayesObj{
  (R:gg)(Y:gg)(W:GG)(B:gg)[Color.PURPLE]:1
 }

The probability that a specific phenotype has been generated can be evaluated with Probability()

>>> print(a0)
BayesObj{
  (R:gg)(Y:gg)(W:GG)(B:gg)[Color.PURPLE]:1/4
  (R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]:1/2
  (R:gg)(Y:gg)(W:gg)(B:gg)[Color.WHITE]:1/4
 }
>>> print(a0.Probability(PickColor(Color.WHITE)))
3/4

Sometimes the parents' genotypes are not known. If one or more offspring have been created using a flower as a parent, then the colors of all these offspring can be used to update the posterior knowledge of the parents' genotypes. This is evaluated using Bayes' theorem.

a2 = a0.Pick(PickColor(Color.WHITE))
>>> print(a2)
BayesObj{
  (R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]:2/3
  (R:gg)(Y:gg)(W:gg)(B:gg)[Color.WHITE]:1/3
 }
>>> print(RoseSeedWhite)
BayesObj{
  (R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]:1
 }
>>> parent0 = a2
>>> parent1 = RoseSeedWhite
>>> child_colors = [Color.WHITE]
>>> a3 = BreedOutcome(parent0,parent1,child_colors)
>>> print(a3)
BayesObj{
  ((R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE], (R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]):3/5
  ((R:gg)(Y:gg)(W:gg)(B:gg)[Color.WHITE], (R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]):2/5
 }

If a flower has unknown genotype, you can also use a function to build a democratic probability for each possible genotype

>>> UnknownGenotype( ('R','Y','W','B'), RosePheno, Color.ORANGE)
BayesObj{
  (B:Gg)(R:GG)(W:Gg)(Y:GG)[Color.ORANGE]:1/9
  (B:Gg)(R:GG)(W:gg)(Y:GG)[Color.ORANGE]:1/9
  (B:Gg)(R:GG)(W:gg)(Y:Gg)[Color.ORANGE]:1/9
  (B:gg)(R:GG)(W:Gg)(Y:GG)[Color.ORANGE]:1/9
  (B:gg)(R:GG)(W:gg)(Y:GG)[Color.ORANGE]:1/9
  (B:gg)(R:GG)(W:gg)(Y:Gg)[Color.ORANGE]:1/9
  (B:gg)(R:Gg)(W:Gg)(Y:GG)[Color.ORANGE]:1/9
  (B:gg)(R:Gg)(W:gg)(Y:GG)[Color.ORANGE]:1/9
  (B:gg)(R:Gg)(W:gg)(Y:Gg)[Color.ORANGE]:1/9
 }

Data Structure

Flower genotypes are saved in a Genotype class instance, which encodes the genes as GenePair class instances. Paired with the data is a dictionary describing the phenotype colors. GenePairs are given one GenePairValue to initialize, which encodes a single genepair ("gg", "Gg", or "GG"). Genotypes are passed as a class with each gene given a key value ("R", "Y", "W", or "B" in the predefined types).

>>> g0 = GenePair(GenePairValue.gg)
>>> print(g0)
gg
>>> print(gpRoseSeedWhite)
{'R': gg, 'Y': gg, 'W': Gg, 'B': gg}
>>> Genotype(gpRoseSeedWhite,pheno={})
(R:gg)(Y:gg)(W:Gg)(B:gg)[]

If the phenotype is defined, then that will show up in the string description too

>>> Genotype(gpRoseSeedWhite,pheno=RosePheno)
(R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]

To evaluate probabilities, the Genotype class is wrapped in a BayesProb class instance wrapper, which includes a probability with the class object (though the code is flexible enough to accept any object rather than only the Genotype class). The BayesProb are collected into a container class, BayesObj, which has a set of probabilities that sum to exactly 1.

>>> b0 = BayesProb(Genotype(gpRoseSeedWhite,pheno=RosePheno),1)
>>> print(b0)
(R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]:1
>>> b1 = BayesObj([b0])
>>> print(b1)
BayesObj{
  (R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]:1
 }

The BayesObj class objects can be accessed through the attribute ".objs". The BayesProb class object is accessed with the attribute ".obj".

>>> b1.objs
[(R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]:1]
>>> b1.objs[0]
(R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]:1
>>> b1.objs[0].obj
(R:gg)(Y:gg)(W:Gg)(B:gg)[Color.WHITE]

Author

• Aaron S. Meyer - asmeyer2012