Simulate CRISPR homing gene drives—adjust homing efficiency and fitness costs to see invasion dynamics
Gene drives are genetic systems that bias inheritance, spreading through populations even when they impose fitness costs. CRISPR-Cas9 homing drives work by converting heterozygotes (w/d) into drive homozygotes (d/d) during reproduction, creating super-Mendelian inheritance.
In the germline of a w/d heterozygote, the Cas9 enzyme (encoded on the drive allele) cuts the wild-type chromosome at the target site. When the cell repairs this break using the drive allele as a template, the wild-type allele is converted to a drive allele. With efficiency e, this converts w/d individuals into d/d before gamete formation.
Unlike purely deleterious mutations, gene drives can invade populations from low frequency if their transmission advantage exceeds their fitness cost. The invasion threshold depends on both homing efficiency (e) and selection coefficient (s). Low-threshold drives (high e, low s) can spread from a single introduced individual.
The time series shows genotype frequencies over generations. Low-threshold drives show rapid spread, while high-threshold drives require sustained releases. The phase diagram plots drive frequency versus fitness cost, revealing stable equilibria and invasion boundaries. The threshold curve shows the minimum initial frequency needed for invasion as a function of drive parameters.