Gene X causes:
- Increased likelihood that children are male
- Infertility of female offspring
Simulation Goals:
- Determine formula for phenotype frequencies of next generation
- Determine formula for amount of iterations to kill population given male birthrate r and initial infection size s.
- Determine variation of mosquito population changes with and without gene X
Simulation Roadmap:
- Run 1: Determine a generalized equation to model generation-to-generation changes in the populations
- Run 2: Gain intuition into general pattern of population decay given an initial state
- Run 3: Gain understanding of model behavior with respect to the variation of a single variable
- Run 4: Graphical extension of Run 3
- Run 5: Gain understanding of model behavior with respect to the variation of 1 variable under differing values of 1 variable
- Run 6: Gain understanding of model behavior with respect to the variation of 2 variables simultaneously (3D graphical extension of Run 5)
Hypotheses:
- Generational breeding patterns follow Hardy-Weinberg ratios
- Iterations
Things Learned:
- % male offspring must be above 50% for gene X to spread faster than it decays.
- Phenotype frequencies follow Hardy-Weinberg Equations.
- Initial population size affects the eventual iteration count
- Iteration vs Growth seems to be f(x) = x^(k) where k < 1
- Iteration vs Initial Population Size seems to be f(x) = k^(-x)
- Iteration vs Initial Infection Rate seems to be f(x) = acot(bx+c)+k
- Iteration vs Ratio seems to be inverse, f(x) = k/x
Sources:
- Mosquito Gene Drive - Where I got the idea for the problem from.
- Hardy Weinberg Equation - The equation I eventually used to model breeding behavior from one generation to the next
- Python 3D Plotting