2c:null 2d:["$","title",null,{"children":"Nested Darwinian populations | Andrew Black | Observable"}] 32:Tac1,{ const container = d3.select(DOM.element('div')); container.style("position", "relative"); const canvas = container.append('canvas').node(); const context = canvas.getContext('2d'); const w = 500; const bar_w = 50; const beta_l = 1.35; const beta_h = 2.0; canvas.width = w; canvas.height = w; var svg = container.append('svg') .attr("width", bar_w) .attr("height", canvas.height) .style("position", "absolute") .style("top", '0px') .style("left", '520px'); beta_scale(svg,w,40,beta_l,beta_h) var margin = ({top: 20, right: 30, bottom: 5, left: 30}) // var mu = 0.025; var cwidth = (w - margin.top - margin.bottom)/((beta_h-beta_l)/0.025) var axis_scale = d3.scaleLinear() .domain([beta_h,beta_l]) .range([margin.top+cwidth/2, w - margin.bottom-cwidth/2]) // marker to show the average growth rate. // svg.append('text').text("-").attr("x",0).attr("y",axis_scale(1.5)) // Vis parameters var space = 40 var scale = 0.01; var pauseAtEnd = 1.5; // Model parameters var beta = Array(100).fill(beta0); var sim_data = []; // var T = 30; var tstep = 0.1; var mu = 0.05; // var p = 0.01; const m1 = 20, m2=20; // const context = DOM.context2d(w, w); // const frames = Math.floor(T/tstep)+1 // const radius = 11.5 const height = w; context.clearRect(0, 0, w, w); var beta_av = d3.mean(beta); var beta_mark = svg.append('circle').attr("cx",5).attr("cy",axis_scale(beta_av)).attr("r",3).style('fill','red') while(true){ // const T = mutable dis; for(let i=0; i<100; i++){ sim_data[i] = pois_approx_dense(beta[i],mutable T,tstep,mu,p) } const frames = sim_data[0].sol1.length; // m loops over the frames for(var m =0; m Math.sqrt(x*scale)) var col = r.b; // draw each circle for(var k=0; k< 3; k++){ context.beginPath(); context.arc((i/10)*w+m1, (j/10)*w+m2, A[k], 0, 2 * Math.PI); context.fillStyle = piyg(col[k]); context.fill(); } c ++; } } yield container.node(); } await Promises.delay(pauseAtEnd*800); // reasmple for next generation beta = dispers_next_gen(sim_data); // update the average beta marker. beta_av = d3.mean(beta) beta_mark.transition().attr("cy",axis_scale(beta_av)) } }33:T4bd,beta_scale = function(svg,h,w,beta_l,beta_h) { // var space = 30 // var scale = 0.001; // var beta_l = 1.3; // var beta_h = 2.0; // const h = 400; // const w = 50 // var svg = d3.select(DOM.svg(w,h)) var mu = 0.025; var b = d3.range(beta_l,beta_h+0.01,mu) var margin = ({top: 20, right: 30, bottom: 5, left: 30}) var piyg = d3.scaleSequential().domain([beta_h,beta_l]).interpolator(d3.interpolateYlGnBu) var swatch_scale = d3.scaleLinear() .domain([beta_l,beta_h+mu]) .range([margin.top, h - margin.bottom]) var cwidth = (h - margin.top - margin.bottom)/((beta_h-beta_l)/mu) var axis_scale = d3.scaleLinear() .domain([beta_h,beta_l]) .range([margin.top+cwidth/2, h - margin.bottom-cwidth/2]) svg.selectAll('rect') .data(b) .enter() .append("rect") .attr("x", 0) .attr("y", d=>swatch_scale(d)) .attr("width",10) .attr("height", cwidth) .attr("fill", d=> piyg(d)) svg.append('g').attr("transform", `translate(${15},0)`) .call(d3.axisRight(axis_scale)) // label svg.append('text').text("β").attr("x",20).attr("y",15) // return svg.node() }34:T5c1,pois_approx_dense = function(beta1,T,tstep, mu,p){ // const beta1 = 1.8; // const beta2 = 1.75; // const beta3 = 1.85; // const mu = 0.05; // const T = 30; // const tstep = 0.2; if (Math.random() < 0.5){ var beta2 = beta1 + mu; var beta3 = beta1 - mu; } else{ beta2 = beta1 - mu; beta3 = beta1 + mu; } const N = Math.pow(10,6); var r = (beta1 -1); var t1 = Math.log(1 - (r/p)*Math.log(1-Math.random()))/r; const n = Math.floor(T/tstep)+1; const sol1 = new Float64Array(n); const sol2 = new Float64Array(n); const sol3 = new Float64Array(n); var t = 0; sol1[0] = 1; sol2[0] = 0; sol3[0] = 0; var i = 1; while (t <= t1){ sol1[i] = Math.exp(r*t); sol2[i] = 0; sol3[i] = 0; t = t + tstep; i++ } var x1 = Math.exp(r*t1); var t2 = t1 + Math.log(1 - (r/p/x1)*Math.log(1-Math.random()))/r; while (t <= t2){ sol1[i] = Math.exp(r*t); sol2[i] = Math.exp((beta2-1)*(t-t1)); sol3[i] = 0; t = t + tstep; i++; } var t3 = Math.floor(t2/tstep)*tstep + tstep; var x3 = [Math.exp(r*t3), Math.exp((beta2-1)*(t3-t1)), Math.exp((beta2-1)*(t3-t2))] var X0 = [N-x3[0]-x3[1]-x3[2],x3[0],x3[1],x3[2]] var ddy = dy(beta1,beta2,beta3,N) s.denseOutput = true; s.solve(ddy,t3,X0,T, s.grid(tstep, (x, y) => {sol1[i] = y[1]; sol2[i] = y[2]; sol3[i] = y[3]; i++})) return {sol1: sol1, sol2:sol2, sol3:sol3, b: [beta1,beta2,beta3]} }35:[] 30:{"id":"842ecabc991dbd3a","slug":"nested-darwinian-populations","title":"Nested Darwinian populations","thumbnail":"1efa566eabafcfc94eb0f3427bd999ff9d24467aa51c1d0944faf5c3acea10b4","access_level":"public","create_time":"$D2019-06-30T02:13:26.585Z","update_time":"$D2020-02-10T23:14:00.549Z","view_time":null,"first_public_time":"$D2019-12-02T06:14:23.600Z","has_unpublished_edits":null,"fork":true,"stars":0,"starred":false,"owner":{"type":"team","id":"95ffc526f2172483","login":"andxblack","name":"Andrew Black","avatar_url":"https://avatars-next.observableusercontent.com/e922b45b1471eadb2bac3f5e8cf0250a5b723865aafeca6bafb9d7144a31c920","tier":"starter_2024","bio":""},"version":1074,"publish_version":1074,"role":null,"authored":false,"authors":[{"type":"individual","id":"5d158442cfe40bae","login":"andxblack","name":"Andrew Black","avatar_url":"https://avatars-next.observableusercontent.com/e922b45b1471eadb2bac3f5e8cf0250a5b723865aafeca6bafb9d7144a31c920","tier":null,"bio":""}],"members":[{"type":"individual","id":"5d158442cfe40bae","login":"andxblack","name":"Andrew Black","avatar_url":"https://avatars-next.observableusercontent.com/e922b45b1471eadb2bac3f5e8cf0250a5b723865aafeca6bafb9d7144a31c920","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Nested Darwinian populations","cells":[{"id":0,"value":"md`# Nested Darwinian populations`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":905,"value":"md`This is a version of the first model presented in the paper: Ecological scaffolding and the evolution of individuality. Andrew J. Black, Pierrick Bourrat & Paul B. Rainey, 2020, Nature Ecology and Evolution, doi: [10.1038/s41559-019-1086-9](https://dx.doi.org/10.1038/s41559-019-1086-9)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":966,"value":"viewof a = {\n const growth_slide = slider({\n min: 1.35,\n max: 2,\n value: 1.8,\n step: 0.05,\n title: 'Initial growth rate',\n})\n const but = growth_slide.appendChild(html``)\n\n but.addEventListener(\"click\", () => {\n mutable beta0 = growth_slide.value });\n \nreturn growth_slide\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":809,"value":"{\n const wrapper = html``;\n const t = wrapper.appendChild(DOM.range(10, 30, 1));\n t.value = mutable T;\n t.oninput = () => {mutable T = t.valueAsNumber;\n wrapper.output.value = mutable T}\n wrapper.append(\n html`30`)\n // if (wrapper.output.value)\n // {\n // wrapper.output.value = 30\n // }\n return wrapper\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":488,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":950,"value":"md`## Explanation\n\n- the dispersal time, T, can be changed with the slider above.\n- the simuaiton can be reset to a new initial rate.\n- The red dot on the color bar shows the average growth rate of the cells in the population.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":642,"value":"md`## Code appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":860,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":689,"value":"dispers_next_gen = function(sol) {\n // return a new list of beta values by sampling the old solutions. \n \n var total_A = [];\n for(var i=0; i<100; i++){\n \n var l = sol[i].sol1.length;\n total_A[i] = sol[i].sol1[l-1] + sol[i].sol2[l-1] + sol[i].sol3[l-1];\n }\n \n // patches to sample from.\n var patch_ind = randsample(total_A,100)\n \n // sample a beta within each patch\n var new_b = Array(100);\n \n for(var i=0; i<100; i++){\n var kn = sol[patch_ind[i]];\n var k2 = [kn.sol1[l-1],kn.sol2[l-1],kn.sol3[l-1]];\n \n var b_index = randsample(k2,1)[0]\n new_b[i] = (sol[patch_ind[i]].b)[b_index]\n }\n \n return new_b\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":681,"value":"randsample = function(weights,num) {\n // var s = Array.from({length: num}, Math.random).sort()\n const sum = weights.reduce((a,b) => a + b, 0)\n const cumSum = weights.map(a => a/sum)\n \n function singleRand(spec) {\n var sum=0, r=Math.random();\n for ( var i = 0; i exports)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":885,"value":"s = new odex.Solver(4);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W35","stdlib":"1"}} 31:"$30:body"