32:T58d,md `Similarly, let's figure what the best strategy is for the Queen bee of the game. She might or might not have such strategy but let's figure nonetheless. We look at the right or the 2nd input within the parentheses. The *best* payout for the queen is strategy (1B, 2X) where the queen mates with the drone that flew all the way to her hive to mate with her. Gotta give some credit to the drone who took his risks right? Let's assume those brave genes and physical strongness to make it all the way to this different hive is what the queen wants in her babies. Hence she gets a payout of 10! Better babies with better genes! The *worst* payout for the queen is strategy (1A,2X) or (1A, 2Y). The Queen has other drone bees that would want to mate with her and hence there are no way ever she will ever lose a payout. We notice that both the worst payout is when the drone plays 1A and doesn't even attempt to mate with her. The queen has nothing to lose as she can mate with another drone that might come by later but in this particular game, she isn't affected at all and hence she has a payoff of 0. Now let's look for the *best responses*. The Queen bee will always end with a better payout if she plays the strategy '2X' where she mates with the drone. Since 0 = 0, both are dominated strategies there but since for when P1 plays 1B: 10 > 5, ** strategy 2X, to mate with the drone is the best strategy. ** ` 33:Tc6c,{ const height = 500 const width = 600 const margin = ({top: 30, right: 40, bottom: 40, left: 50}) const svg = d3.select(DOM.svg(width, height)) const pie = d3.pie() .value((d) => d.value) const arc = d3.arc() .innerRadius(0) .outerRadius(50) const arc_out = d3.arc() .innerRadius(0) .outerRadius(53) svg.append('line') .style("stroke", "lightgray") .style("stroke-width", 5) .attr("x1", 180) .attr("y1", 75) .attr("x2", 180) .attr("y2", 165) svg.append('line') .style("stroke", "lightgray") .style("stroke-width", 5) .attr("x1", 120) .attr("y1", 75) .attr("x2", 240) .attr("y2", 75) ////// father, mother, focal ////// for(var x=0; x<3; x++){ var gr = 'g' + x.toString() gr = svg.append('g').join(DATA.data)//svg.selectAll("g").data(DATA).join("g") .attr('transform', 'translate(' + DATA[x].transx*width/10 + ',' + DATA[x].transy*height/10 + ')') svg.append("text") .attr("x", DATA[x].transx*width/10 - 30 ) .attr("y", DATA[x].transy*height/10 + 70) .attr("font-size", 15) .text(DATA[x].label) var color = d3.scaleOrdinal() .domain(DATA[x].dataset) .range(DATA[x].colors) const part = gr.selectAll('.part') .data(pie(d3.entries(DATA[x].dataset))) .enter() .append('g') part.append('path')//up .attr('d', arc) .attr('class', (d,i)=>d.data.key) .attr("stroke", "white") .attr('stroke-width', '2') .attr('fill', (d, i) => color(i)) } console.log((d,i)=>d.key) ////// checkbox relatives ////// if(check.length>0){ for(var y=3; yd.data.key) .attr('d', arc) .attr("stroke", "white") .attr('stroke-width', '2') .attr('fill', (d, i) => color(i)) } } svg.selectAll('path') .style('cursor','pointer') .on("mouseover", function(d) { d3.select(this) .attr('d',arc_out) svg.selectAll('path.'+ d.data.key) .attr('d',arc_out) }) .on("mouseout", function(d) { d3.select(this) .attr('d',arc) svg.selectAll('path.'+ d.data.key) .attr('d',arc) }) return svg.node(); } 34:T71a,{ //A: '#329215', B: red , C: c1, D: black, E:c2, F:white var string = 'Relatedness: '; while(DATA_new.length > 0) { DATA_new.pop(); } if(check.length>0) { if(check.includes("ss")) {DATA_new.push({ label: "supersister", transx: 1, transy: 4.5, generation: 2, dataset: {'B': 0.5, 'A':0.25, 'E': a2/4, 'C':a1/4}, colors: ["red","#329215", c2, c1], line: [180,125,60,165]}) string += "super sister:75% " } if(check.includes("b")) {DATA_new.push({ label: "brother", transx: 5, transy: 4.5, generation: 2, dataset: {'C': a1/4, 'E': a2/4, 'F':0.5, 'A':0.25}, colors: [c1, c2, "white","#329215"], line: [300,125,300,165]}) string += " brother:25% " } if(check.includes("hs")) {DATA_new.push({ label: "half sister", transx: 7, transy: 4.5, generation: 2, dataset: {'C': a1/4, 'E': a2/4, 'D':0.5, 'A':0.25}, colors: [c1, c2, "black","#329215"], line: [420,75,420,165]}) string += " half sister:25% " } if(check2.includes("fn")) {DATA_new.push({ label: "full nephew", transx: 1, transy: 8, generation: 3, dataset: {'C': a1/8, 'E': a2/8, 'B':0.25, 'F':0.5, 'A': 0.125}, colors: [c1, c2, "red", "white","#329215"], line: [60,300,60,340]}) string += " full nephew:37.5% " } if(check.includes("s")) {DATA_new.push({ label: "son", transx: 3, transy: 8, generation: 3, dataset: {'B': 5, 'A': 5, 'F':10}, colors: ["red", "#329215", "white"], line: [180,300,180,340]}) string += " son:50% " } if(check2.includes("hn")) {DATA_new.push({ label: "half nephew", transx: 7, transy: 8, generation: 3, dataset: {'C': a1/8,'E': a2/8, 'D':0.25, 'F':0.5, 'A':0.125}, colors: [c1, c2, "black", "white","#329215"], line: [420,300,420,340]}) string += " half nephew:12.5% " } } return string; }35:T8e1,function input(config) { let { form, type = "text", attributes = {}, action, getValue, title, description, format, display, submit, options } = config; const wrapper = html`

`; if (!form) form = html``; Object.keys(attributes).forEach(key => { const val = attributes[key]; if (val != null) form.input.setAttribute(key, val); }); if (submit) form.append( html`` ); form.append( html`` ); if (title) form.prepend( html`

${title}

` ); if (description) form.append( html`

${description}

` ); if (format) format = typeof format === "function" ? format : d3format.format(format); if (action) { action(form); } else { const verb = submit ? "onsubmit" : type == "button" ? "onclick" : type == "checkbox" || type == "radio" ? "onchange" : "oninput"; form[verb] = e => { e && e.preventDefault(); const value = getValue ? getValue(form.input) : form.input.value; if (form.output) { const out = display ? display(value) : format ? format(value) : value; if (out instanceof window.Element) { while (form.output.hasChildNodes()) { form.output.removeChild(form.output.lastChild); } form.output.append(out); } else { form.output.value = out; } } form.value = value; if (verb !== "oninput") form.dispatchEvent(new CustomEvent("input", { bubbles: true })); }; if (verb !== "oninput") wrapper.oninput = e => e && e.stopPropagation() && e.preventDefault(); if (verb !== "onsubmit") form.onsubmit = e => e && e.preventDefault(); form[verb](); } while (form.childNodes.length) { wrapper.appendChild(form.childNodes[0]); } form.append(wrapper); return form; }36:T408,function checkbox(config = {}) {var show;// = 'disabled';//holly${show} let {value: formValue, title, description, submit, options} = config; if (Array.isArray(config)) options = config; options = options.map(o => typeof o === "string" ? {value: o, label: o, show:o} : o); const form = input({ type: "checkbox", title, description, submit, getValue: input => { if (input.length) return Array.prototype.filter.call(input, i => i.checked).map(i => i.value); return input.checked ? input.value : undefined; }, form: html` ` }); form.output.remove(); return form; }37:[{"id":"29e78c954601177d770e88131f095ac608a6832878705983226ee4d0a527ebcc83c40c891d32299ad976fe7785ddf29f6b1b82bbf17c5fecb0b5556b0b6c78e3","href":"https://static.observableusercontent.com/files/29e78c954601177d770e88131f095ac608a6832878705983226ee4d0a527ebcc83c40c891d32299ad976fe7785ddf29f6b1b82bbf17c5fecb0b5556b0b6c78e3","name":"Bee-jumping-over-flowers.gif","type":"image/gif","lastModified":1613588576684.543,"size":1104444}] 30:{"title":"Why bees help siblings before the need of them to try and reproduce - MERGED UPDATED","cells":[{"id":0,"value":"md`# Why bees help siblings before the need of them to try and reproduce - MERGED UPDATED `","pinned":false,"hidden":false,"mode":"ojs"},{"id":25,"value":"md` In this game matrix, there are 2 players: the drone (player 1 and player on left) and the queen that the drone wants to mate with (player 2 and player on top).\n\nThe Drone has 2 strategies. It can either \n- stay within its pollinator community (Strategy A) or \n- it can fly off to try to mate with the queen he wants to mate with(Strategy B). \n\nOf course, there is no guarantee he can mate even if he leaves his community.\n\nThe Queen has 2 strategies as well. It can either \n- mate with the drone (Strategy X) or \n- it can not mate with the drone. (Strategy Y). `","pinned":false,"hidden":false,"mode":"ojs"},{"id":21,"value":"md `\nFor some insight,\n\na drone bee can either stay within its colony to help his siblings or try his best to mate with a queen bee of another colony.\n\nIf it stays within its colony, he will benefit from the reproductive benefit of his siblings laying more potential workers, and hence him swarming in the abundance of excessive resources within the community.\n\nHowever, if the drone becomes ambitious enough to try and spread its genetics and mate with another queen, it will die in the moment of mating.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":408,"value":"//Thanks to the links below\n//https://observablehq.com/@ruohan-huang/howls-moving-castle\n//https://www.w3schools.com/howto/howto_js_slideshow.asp\n\nviewof selectedWallpaper = slideshow({\n title: 'Bee Plays - (And applied strategy)',\n description: 'Slideshow:',\n options: Beeadobe.map(wallpaper => ({\n label: wallpaper.name,\n value: wallpaper.url\n }))\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":406,"value":"md`![pic](${selectedWallpaper})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":12,"value":"{\n const matrix = [\n ['Payoff Matrix', '2X (mate)', '2Y (do not mate)'],\n [ '1A (stay)', '(10,0)', '(10, 0)'],\n [ '1B (leave)', '(5,10)', '(-10, 5)']\n ];\n\n const div = html`

`; \n \n const tr = d3.select(div)\n .append(\"table\")\n .selectAll(\"tr\")\n .data(matrix)\n .join(\"tr\");\n\n const td = tr.selectAll(\"td\")\n .data(d => d)\n .join(\"td\")\n .text(d => d);\n\n return div;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":36,"value":"md `Let's try to understand the payoff matrix for the drone.\n\n- The *best* payout for him is strategy (1A, 2X) where he gets a payout of 10. \n- The *worst* payout for him is strategy (1B, 2Y) where he loses a payout and ends up with -10.\n\nTo make things easier, by looking for *best responses*, we realize that the payouts for player 1 are always greater once he plays the strategy '1A'. \n\nWe notice this as 10>5 when player 2 plays strategy 2X, and also since 10>-10 when player 2 plays strategy 2Y. \n\nHence for Player 1 (the drone), his **best strategy is to play 1A and stay within its pollinator community.**\n\n` ","pinned":false,"hidden":false,"mode":"ojs"},{"id":488,"value":"athomebee = FileAttachment(\"Bee-jumping-over-flowers.gif\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":491,"value":"md `## Understanding payout results`","pinned":false,"hidden":false,"mode":"ojs"},{"id":56,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":483,"value":"md ` With Game Theory, we were able to practically see why drone bees would be smarter to help out their own sister worker sibling bees rather than be 'ambitious' and go out to try and mate a queen bee. Below, provides a more conceptual approach to see how related bee siblings are in a typical bee family and provides a number approach to their relativity. `","pinned":false,"hidden":false,"mode":"ojs"},{"id":500,"value":"md ` ## Interactive tool that measures relativity between bee families `","pinned":false,"hidden":false,"mode":"ojs"},{"id":536,"value":"md`This interactive tool shows the genetic relationships between bee's family members. Because of the difference in male(haploid, or single set of chromosomes) and female(diploid, or two sets of chromosomes) bees' genetic behavior, the relatedness between each family member is different. This tool uses the bees' family tree and their genetic compositions, which are represented on pie charts, to show the **relatedness** of each family member **with the focal-worker**.\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":514,"value":"md` To use this interactive tool, try these:\n - Select specific relatives to show on the family tree\n - Select \"Super Sister\" to enable \"Full Nephew\n - Select \"Half Sister\" to enable \"Half Nephew\" \n - Set up mom's genes using the slider; observe how her genes affect the family\n - Hover over the graph to see the genetic similarities between each relative\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":455,"value":"viewof check = checkbox({\n title: 'Relatives',\n description: 'Select relatives to show',\n options: [\n { value: 'ss', label: 'Super Sister'},\n { value: 'hs', label: 'Half Sister'}, \n { value: 'b', label: 'Brother'},\n { value: 'fn', label: 'Full Nephew',display: 'none' },\n { value: 's', label: 'Son' },\n { value: 'hn', label: 'Half Nephew',display: 'none' },//\"inline-block\"\n ],\n value: []\n \n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":457,"value":"viewof check2 = checkbox({\n //title: 'Relative',\n description: 'Select relatives to show',\n options: [\n { value: 'fn', label: 'Full Nephew', show:disable_fn},\n { value: 'hn', label: 'Half Nephew', show:disable_hn},//,show: 'disabled'\n ],\n value: []\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":459,"value":"viewof c1 = color1()","pinned":false,"hidden":false,"mode":"ojs"},{"id":461,"value":"viewof a1 = slider({\n min: 0, \n max: 1, \n value: 1,\n step: 0.01, \n format: \".0%\",\n description: \"Set up mom's genes\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":463,"value":" viewof c2 = color2()","pinned":false,"hidden":false,"mode":"ojs"},{"id":465,"value":"viewof a2 = slider({\n value: 1-a1,\n format: \".0%\",\n description: \"Set up mom's genes\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":467,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":526,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":671,"value":"md`## Understanding the results`","pinned":false,"hidden":false,"mode":"ojs"},{"id":636,"value":"md`\nDid you observe the following relatedness of the focal-worker and each family member?\n\n Relatedness:\n - Super-sister: 75%\n - Son:50% \n - Brother: 50%\n - Half sister:25% \n - Full nephew:37.5% \n - Half nephew:12.5%\n\nAs can be seen, the relatedness between the focal-worker and each family member varies. We can see that the focal-worker shares more genetic similarities with her sister(75%) than with her own son(50%)! This concludes why focal-workers will most likely help out their sister worker sibling bees, rather than taking care of their own sons. The 75% genetic similarity also explains why these sister worker bees are called \"super-sisters.\" \n`\n\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":627,"value":"md`## References`","pinned":false,"hidden":false,"mode":"ojs"},{"id":478,"value":"//Ian's code","pinned":true,"hidden":false,"mode":"ojs"},{"id":11,"value":"d3 = require(\"d3@5\", \"d3-hexbin\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":67,"value":"dotStyles = ({ defaults: `\n graph [\n labelloc = \"b\",\n fontname=\"Times\",\n fontsize=12,\n overlap=false ];\n\n node [\n style=filled,\n shape=circle,\n colorscheme=accent5,\n color=1,\n fontname=\"Times\",\n fontsize=12];\n\n edge [\n fontname=\"Times\",\n fontsize=12,\n margin=2,\n overlap=false ];\n` })","pinned":false,"hidden":false,"mode":"ojs"},{"id":69,"value":"dot = {\n const Viz = await require(\"https://unpkg.com/viz.js@1.8.0/viz-lite.js\").catch(() => window.Viz);\n return function(strings) {\n let string = strings[0] + \"\", i = 0, n = arguments.length;\n while (++i < n) string += arguments[i] + \"\" + strings[i];\n string = Viz(string);\n return html([string.slice(string.indexOf(\" Math.round(input.valueAsNumber * precision) / precision;\n return input({\n type: \"range\",\n title,\n description,\n submit,\n format,\n display,\n attributes: { min, max, step, disabled, value },\n getValue\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":444,"value":"function color1(config = {}) {\n const { value = \"#c3c2b2\", title, description, disabled, submit, display } =\n typeof config === \"string\" ? { value: config } : config;\n const form = input({\n type: \"color\",\n title,\n description,\n submit,\n display,\n attributes: { disabled, value }\n });\n // The following two lines are a bugfix for Safari, which hopefully can be removed in the future.\n form.input.value = '';\n form.input.value = value;\n if (title || description) form.input.style.margin = \"5px 0\";\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":446,"value":"function color2(config = {}) {\n const { value = \"#fd9621\", title, description, disabled, submit, display } =\n typeof config === \"string\" ? { value: config } : config;\n const form = input({\n type: \"color\",\n title,\n description,\n submit,\n display,\n attributes: { disabled, value }\n });\n // The following two lines are a bugfix for Safari, which hopefully can be removed in the future.\n form.input.value = '';\n form.input.value = value;\n if (title || description) form.input.style.margin = \"5px 0\";\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":448,"value":"md` Input Checkbox from: https://observablehq.com/@jashkenas/inputs`","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W37","stdlib":"1","titling":"auto"}