Stochhastic elements

In the Wright-Fisher model, the 2Ncopies of a locus in consideration could come eitherfromNdiploidindividuals (who have two copies of their genetic material in each cell) or2Nhaploidindividuals (who have one copy of their genetic material in each cell). ConsiderMoran modelwithonetype of mutation. We think ofn= 2N haploid individuals, anda genetic locus with two allelesAandathat have the same fitness. This model evolvesacoording to the following rules:
(i) At each time step, an individualxis chosen uniformly at random out ofnindividuals.We want to replacexwith a clone.
(ii) For this, we “clone” an individual chosen at random from the set of allnindividuals,includingxitself. Then, we replacexwith the clone.
(iii) A specific mutation may occur during cloning. If we are cloning alleleA, then it maymutate to alleleawith probability 0

 

Sample Solution

On the cusp of World War Two FDR runs against and defeats Wendell Wilkie, the Republican nominee for president. This election is key not only due to the events taking place in Europe, but also because of the fact that FDR has now gone against the precedent set by George Washington. Despite heavy campaigning the republicans are unable to dethrone Roosevelt. Roosevelt insisted throughout his campaign that he was only in the race to keep America out of the war in Europe. However, due to the way things unfolded, he would soon be forced to intervene. FDRs third term was dominated by World War Two. Due to the influence of isolationists FDR was unwilling and unable to enter the war immediately. This meant that despite not getting involved in the fighting, the United States would commit to arming and aiding its allies in their fight against the axis powers. Therefore, as Churchill put it, FDR had committed to a policy of “all aid short of war.” In the first of many highly secretive meetings, Roosevelt and Churchill met in August 1941. The outcome of this meeting was the Atlantic Charter, a pivotal piece of conceptual legislature that outlined global wartime and post-war goals. Despite constant pressure from Churchill, FDR did not believe that congress would allow the United States to enter the war. For the time being, the role undertaken by the United States was that of aid and protection, not of direct intervention. However, this would not last very long. Despite the primary concern being the European theatre, Japan also presented a serious challenge. Following the Japanese conquest of South East Asia, FDR decides to stop selling them oil, depriving Japan of 95% of its oil supply. FDR also placed General Douglas MacArthur as the commander of the American forces in the Philippines. When diplomatic efforts failed to lift the embargo, the Japanese felt forced into action; believing that if they were able destroy the US pacific fleet, along with its naval forces stationed in South East Asia, they would be able to continue their conquests. Therefore, on

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