import csv
import itertools
import sys
PROBS = {
# Unconditional probabilities for having gene
"gene": {
2: 0.01,
1: 0.03,
0: 0.96
},
"trait": {
# Probability of trait given two copies of gene
2: {
True: 0.65,
False: 0.35
},
# Probability of trait given one copy of gene
1: {
True: 0.56,
False: 0.44
},
# Probability of trait given no gene
0: {
True: 0.01,
False: 0.99
}
},
# Mutation probability
"mutation": 0.01
}
def main():
# Check for proper usage
if len(sys.argv) != 2:
sys.exit("Usage: python heredity.py data.csv")
people = load_data(sys.argv[1])
# Keep track of gene and trait probabilities for each person
probabilities = {
person: {
"gene": {
2: 0,
1: 0,
0: 0
},
"trait": {
True: 0,
False: 0
}
}
for person in people
}
# Loop over all sets of people who might have the trait
names = set(people)
for have_trait in powerset(names):
# Check if current set of people violates known information
fails_evidence = any(
(people[person]["trait"] is not None and
people[person]["trait"] != (person in have_trait))
for person in names
)
if fails_evidence:
continue
# Loop over all sets of people who might have the gene
for one_gene in powerset(names):
for two_genes in powerset(names - one_gene):
# Update probabilities with new joint probability
p = joint_probability(people, one_gene, two_genes, have_trait)
update(probabilities, one_gene, two_genes, have_trait, p)
# Ensure probabilities sum to 1
normalize(probabilities)
# Print results
for person in people:
print(f"{person}:")
for field in probabilities[person]:
print(f" {field.capitalize()}:")
for value in probabilities[person][field]:
p = probabilities[person][field][value]
print(f" {value}: {p:.4f}")
def load_data(filename):
"""
Load gene and trait data from a file into a dictionary.
File assumed to be a CSV containing fields name, mother, father, trait.
mother, father must both be blank, or both be valid names in the CSV.
trait should be 0 or 1 if trait is known, blank otherwise.
"""
data = dict()
with open(filename) as f:
reader = csv.DictReader(f)
for row in reader:
name = row["name"]
data[name] = {
"name": name,
"mother": row["mother"] or None,
"father": row["father"] or None,
"trait": (True if row["trait"] == "1" else
False if row["trait"] == "0" else None)
}
return data
def powerset(s):
"""
Return a list of all possible subsets of set s.
"""
s = list(s)
return [
set(s) for s in itertools.chain.from_iterable(
itertools.combinations(s, r) for r in range(len(s) + 1)
)
]
def joint_probability(people, one_gene, two_genes, have_trait):
"""
Compute and return a joint probability.
The probability returned should be the probability that
* everyone in set `one_gene` has one copy of the gene, and
* everyone in set `two_genes` has two copies of the gene, and
* everyone not in `one_gene` or `two_gene` does not have the gene, and
* everyone in set `have_trait` has the trait, and
* everyone not in set` have_trait` does not have the trait.
"""
prob = 1
for person in people:
if person in two_genes:
allele_num = 2
elif person in one_gene:
allele_num = 1
else:
allele_num = 0
trait = person in have_trait
mother = people[person]['mother']
father = people[person]['father']
# If there is no information on the parents
if mother is None and father is None:
prob *= PROBS['gene'][allele_num]
# Otherwise calculate probability from parents
else:
inherit = {}
for parent in [mother, father]:
if parent in two_genes:
inherit[parent] = 1 - PROBS['mutation']
elif parent in one_gene:
inherit[parent] = 0.5
else:
inherit[parent] = PROBS['mutation']
if allele_num == 2:
prob *= inherit[mother] * inherit[father]
elif allele_num == 1:
prob *= (inherit[mother] * (1 - inherit[father])) + ((1 - inherit[mother])*(inherit[father]))
else:
# if allele_num is 0
prob *= (1 - inherit[mother]) * (1 - inherit[father])
prob *= PROBS['trait'][allele_num][person in have_trait]
return prob
def update(probabilities, one_gene, two_genes, have_trait, p):
"""
Add to `probabilities` a new joint probability `p`.
Each person should have their "gene" and "trait" distributions updated.
Which value for each distribution is updated depends on whether
the person is in `have_gene` and `have_trait`, respectively.
"""
for person in probabilities:
if person in two_genes:
genes = 2
elif person in one_gene:
genes = 1
else:
genes = 0
probabilities[person]['gene'][genes] += p
probabilities[person]['trait'][person in have_trait] += p
def normalize(probabilities):
"""
Update `probabilities` such that each probability distribution
is normalized (i.e., sums to 1, with relative proportions the same).
"""
norm_prob = probabilities.copy()
for person in probabilities:
for field in ['gene', 'trait']:
total = sum(dict(probabilities[person][field]).values())
for value in probabilities[person][field]:
norm_prob[person][field][value] = probabilities[person][field][value] / total
return norm_prob
if __name__ == "__main__":
main()
