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I'm not sure I understand the question. You've elegantly demonstrated that only a tiny fraction of all protein sequences could possibly exist, but then asked why only a tiny fraction of all protein sequences do exist. Your conclusions about independent origins of life having no proteins in common are accurate, but also consider that you as a human being have ...


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The answer is chance or, even better, contingency. About your calculations, it is true that the theoretical sequences are almost unlimited, but the basic scaffolds are not. Very different sequences can fold into the same basic scaffold and have a similar reactivity/function. So, even if not all the sequences have been explored on this planet, most of the ...


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Let's take the opposite extreme, $K=0$, so that each site has an independent effect on fitness. Without loss of generality, we can say that at each locus $n$, the $1$ allele confers an advantage $s_n$ over the $0$ allele. Then there is just one local optimum, the global optimum, at $\vec{1}$, so $M_1=1$ (and $P_m=2^{-N}$). The key difference is that in the ...


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I am not sure what your question is but here is an example that may interest you. The three sunflower species Helianthus anomalus, H. deserticola, and H. paradoxus are all of hybrid origin of the same two "parent species" (H. annuus and H. petiolaris). Major ecological transitions in wild sunflowers facilitated by hybridization is a paper that will ...


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One example of what you may consider to be a macroevolutionary change is a whole-genome-duplication, or polyploidy event. These are not uncommon in plants, and can promote speciation due to a reproductive barrier arising between the polyploid progeny and the diploid parents. You can find many papers about this topic, here is one from 2009: ...


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First of all, there is a very heated debate about this in the field of social evolution at present, and you aren't likely to get a conclusive answer. One theorist may give you one answer, but another will vehemently disagree. I'll start by logically answering your questions in reverse order! Question 2: Can you please provide an intuitive explanation of why ...


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Noting that the right hand side can also be written $\mathbf{G}\mathbf{P}^{-1}\mathbf{s}$, we see that the only theoretical limitation of the multivariate breeders equation is the invertibility of the matrix $\mathbf{P}$. This happens when the measures of two traits are the same for all individuals, making two columns of the matrix the same I.e. It becomes ...


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His notion of systemic mutations involved the postulation of massive chromosomal rearrangements (not mere recombination/crossing-over) as mediators of speciation in one-step. While whole genome duplications have been shown to induce speciation (see, for example, cryptic speciation in Hyla versicolor) they are not large scale rearrangements as he suggested. ...



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