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Is this the exact text from the book? The left side seems to represent the probability for "No coalescence in $k$ lines in $t$ generations (i.e. the $Pr(k)^t$ term), and at least one coalescence among those lines in generation $t+1$ (the $1-Pr(k)$ term)" which is the same event as "First coalescence event in $k$ lines is exactly in generation ...


1

Not in general -- there can be linkage disequilibrium among the loci. For instance, say that there are two di-allelic loci, $A/a$ and $B/b$, and that the frequencies of the $A$ and $B$ alleles are both $1/2$ and that they have the same effect on the trait, with no dominance. If all haplotypes in the population are either $Ab$ or $aB$ (with no $AB$ or $ab$ ...


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Well, the total genetic variance is just, by the definition of the variance, $$ \sigma^2 =\sum_{i,j} f_i f_j (w_{ij}-\bar{w})^2 $$ (using $f_i$ and $w_{ij}$ for frequency and fitness, respectively), and $$\bar{w} = \sum_{i,j} f_i f_j w_{ij}$$ is just the average fitness. You can calculate the additive genetic variance for different loci by simply assuming ...


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Hopefully this syllogism will answer your question. Given the following premises: In the absence of selection, fitness of individuals are at a theoretical maximum. If a theoretical maximum fitness is achieved then effective population size is maximum. If there is an allele that confers both increased and decreased fitness you have a genetic conflict (e.g. ...


3

To a good first approximation $\overline{\Delta f} = 0$. Where $\overline{\Delta f}$ is the mean change in fitness down to any point or indel mutation. The reasons for this are as follows: In the genome of higher organisms, most of the genome is non-functional ("junk") so most mutations will not have any effect regardless of the change made. A substantial ...


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I don't believe you can produce a general function for this. It will depend on the exact gene and organism you are considering. From a molecular point of view, the vast majority of recessive mutations result from a change producing either a non-functional protein product or a truncated product that is cleaned up by the cell. We can reasonably assume that ...


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[This is purely speculative] Assumptions: impact on fitness is measured by survival chance impact is because of protein coding genes Probability of a mutation at position $i$ $P(m=i\ |\ g)$ where $g$ is the genome with its annotations. Probability that activity of some protein changes by X-fold given mutation at $i^{th}$ position(s) in the genome: ...


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An easy way to visualize the mistake in your thought experiment is to consider a bottleneck event, when the ancestral population was very small, maybe just a few individuals. This would mean that the entire current population is descending from just a few individuals. Your thought experiment is assuming that the "pyramid" of your ancentors is expanding all ...


3

Your calculations are the following. Assuming non-overlapping generations, the number of ancestors you have in the last $t$ generation is given by: $$\sum_{i=1}^t 2^t$$ This sounds correct. But there are some very strong assumptions: Generations are non-overlapping. A more realistic model would need to consider $t$ as a continuous variable a give a ...


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Here is my full derivation to the book example you gave, hopefully it'll help you clear up what went wrong: You need to remember that after there is selection acting on the population, you no longer have a total of 1 after selection. Think of selection as "killing" individuals, which means the total is now 1 minus what has been "selected out". s*y is what ...



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