Nature, in Code

Genetic Drift: The Effect of Population Size

Genetic drift is the change in allele frequencies due to random chance events. The graphs below shows 10 simulation runs each, where the frequency of a neutral allele fluctuates over 200 generations. The simulations are based on a "one locus, two alleles" model, and p denotes the frequency of one of the alleles.

The first graph shows the evolutionary dynamics of a population of size N=20. By generation 200, all populations have usually lost one of the two alleles:

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The effect of drift is strongly dependent on the population size N. In larger populations, the effect of drift is weaker, as can be seen in the graph below where N = 200:

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And N = 2000:

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Code

var p;
var N = 20; // change this to see effect
var generations = 200;
var data = [];
var simulations = 10;


function next_generation(simulation_data) {
	var draws = 2 * N;
	var a1 = 0;
	var a2 = 0;
	for (var i = 0; i < draws; i = i + 1) {
		if (Math.random() <= p) {
			a1 = a1 + 1;
		}
		else {
			a2 = a2 + 1;
		}
	}
	p = a1/draws;
	simulation_data.push(p);
}

function simulation(simulation_counter) {
	p = 0.5;
	for (var i = 0; i < generations; i = i + 1) {
		next_generation(data[simulation_counter]);
	}
}

for (var i = 0; i < simulations; i = i + 1) {
	data.push([]);
	simulation(i);
}

draw_line_chart(data,"Generation","p",["Population Size:",N,"Generations:",generations]);
			

Note: the draw_line_chart function is built with D3.js and can be found here.