Theorem of independent probabilities. The probability of inheriting multiple traits simultaneously equals the product of the individual marginal probabilities (Pi) of each gene.
Binomial Expansion (F2)
(43D+41r)n
Expected phenotypic distribution when crossing heterozygotes, where D is the dominant trait, r the recessive, and n the number of genes. For n=2, this yields the classic 9:3:3:1 ratio.
Combinatorial Complexity
Genotypes=3n∣Phenotypes=2n
The state space grows exponentially based on the heterozygous genes involved (n). A 4-gene cross (tetrahybrid) generates exactly 81 possible genotypes and 16 observable phenotypes.
1. Law of Segregation (1st Law)
During gamete formation (meiosis), the two alleles for a given gene separate (segregate) from each other so that each gamete carries only one allele for each gene. In a heterozygous individual (Aa), the probability of transmitting either A or a is exactly 50%.
2. Law of Independent Assortment (2nd Law)
States that alleles of two (or more) different genes get sorted into gametes independently of one another. In other words, inheriting the trait for seed color does not affect the probability of inheriting the trait for seed texture. This biological law justifies the use of the Product Rule in our mathematical engine.
3. Limitations of the Ideal Classic Model
This simulator recreates the perfect theoretical conditions of the original 19th-century experiments. To apply this to complex organisms, these exceptions must be considered:
①Complete Dominance: The model assumes the heterozygote (Aa) completely masks the recessive allele. It does not account for incomplete dominance (blended traits) or codominance (e.g., blood types).
②No Genetic Linkage: We assume genes are located on different chromosomes or far apart. If two genes are physically close (linked), they will travel together, breaking the independent assortment expected by the Second Law.
③Epistasis and Lethality: The model ignores interactions where one gene suppresses another (epistasis) or lethal alleles that cause embryonic mortality, skewing the expected mathematical ratios.