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R5099/3_Project_inherited_division_death_hist.html
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<!DOCTYPE html>
<html>
<head>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
</head>
<div id="tester" style="width:0px;height:-100px;"></div>
<div id="myDiv"></div>
</head>
<body>
<script>
// initiation of variables
var division_rate = 1/150; //per minutes
var killing_rate = 1/150; //per minutes
var N = 15; // initial population size
var noise_division=0.01;
var noise_killing=0.01;
var time_lapse_in_minutes = 1000; // duration of the simulation
var simulations = 2000;
var data = [];
var growth_rates= [];
// create a new bacterium
function new_bacterium(div_rate){
// inherited division rate (not killing rate)
if (div_rate != undefined) {
var new_bact = { individual_division_rate: div_rate, individual_killing_rate: 1/random_from_normal_distribution(1/killing_rate,noise_killing * (1/killing_rate))};
return new_bact;
}
// random division rate
else {
var new_bact = { individual_division_rate: 1/random_from_normal_distribution(1/division_rate, noise_division * (1/division_rate)), individual_killing_rate: 1/random_from_normal_distribution(1/killing_rate, noise_killing * (1/killing_rate))};
return new_bact;
}
}
// kill a bacterium
function kill_bacterium(index,bacterium_to_kill){
bacterium_to_kill.splice(index,1);
}
//uses Box-muller transform to get normal random variables from uniform random variables
//https://theclevermachine.wordpress.com/2012/09/11/sampling-from-the-normal-distribution-using-the-box-muller-transform/
function random_from_normal_distribution(mean, variance) {
var u1 = Math.random(); // should belong to ]0,1]
if (u1 == 0){
u1 = 1;
}
var u2 = Math.random(); // should belong to ]0,1]
if (u2 == 0){
u2 = 1;
}
theta = 2 * 3.14 * u2;
var r = Math.sqrt(-2 * Math.log(u1));
var x = r * Math.cos(theta);
var y = r * Math.sin(theta);
x = mean + Math.sqrt(variance) * x;
// return only one of the two normal random variable generated
return x;
}
// calculate the population size for each time step
function next_time_step(current_N) {
var next_N = current_N; // creates a copy directly because it is a primitive value
var temp_bacterium = [];
temp_bacterium = bacterium.slice(0); // creates a copy - not the reference of the array.
var all_bacterium_to_kill=[];
for (var i = 0; i < current_N; i++){
//Divide cells with a frequency of "individual_division_rate"
if (binomial_draws(1,bacterium[i].individual_division_rate) == 1){
temp_bacterium.push(new_bacterium(bacterium[i].individual_division_rate)); // division rate IS inherited
next_N = next_N + 1;
}
//kills cells with a frequency of "individual_killing_rate"
if (binomial_draws(1 , bacterium[i].individual_killing_rate) == 1){
all_bacterium_to_kill.push(i);
}
}
// kill them all at once otherwise the index changes
for (var i = all_bacterium_to_kill.length-1; i >= 0 ; i--){
kill_bacterium(all_bacterium_to_kill[i],temp_bacterium);
next_N = next_N - 1;
}
bacterium = temp_bacterium;
return next_N;
}
function binomial_draws(n,p){
var number_of_success = 0;
for (var i = 0; i < n; i++){
var random_number = Math.random();
if (random_number < p){
number_of_success = number_of_success + 1;
}
}
return number_of_success;
}
// calculate the final population size for each simulation
function simulation(simulation_counter) {
var population_sizes = [];
population_sizes.push(N);
// calculate the intermediate population sizes for each simulation
for (var i = 0; i < time_lapse_in_minutes; i++){
var new_N = next_time_step(population_sizes[i]);
population_sizes.push(new_N);
if (new_N > 1000){ // in order to limit computation time, stop if population size is bigger than 1000
break;
}
}
// in case I want to compare the growth rates between different simulations - I do not use it now
var sum_of_growth_rates = 0 ;
for (var i = 0; i < population_sizes[time_lapse_in_minutes]; i++){
sum_of_growth_rates += bacterium[i].individual_division_rate;
}
average_growth_rate = sum_of_growth_rates/population_sizes[time_lapse_in_minutes];
return [population_sizes, average_growth_rate];
}
// run all simulations
function run_simulations(){
for (var i = 0; i < simulations; i++) {
bacterium =[];
for (var ii = 0; ii < N; ii++){
bacterium.push(new_bacterium());
}
output_simulation = simulation(i);
population_sizes = output_simulation[0];
//average_growth_rate = output_simulation[1];
data.push(population_sizes);
//growth_rates.push(average_growth_rate);
}
}
run_simulations();
var final_population_inherited=[];
for (var i=0; i<simulations; i++){
final_population_inherited.push(data[i][time_lapse_in_minutes]);
}
var dataPopInherited = {
x: final_population_inherited,
type: 'histogram',
name: "Inherited",
opacity: 0.5,
marker: {
color: 'blue',
},
};
var data_hist = [dataPopInherited ];
var layout = {
barmode: "overlay",
title: "Survival",
xaxis: {title: "Final Population Size"},
yaxis: {title: "Count"}
};
Plotly.newPlot('myDiv', data_hist, layout);
</script>
</body>
</html>
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