A Mathematician's Approach to Evolution Theory

Depth of thought.

 

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And yet you remain so shallow.

 

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Is this all you have pad ? Just a shallow response?

 

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Probably makes no difference, but that "incredibly well-verified empirical observation" is false, in general.

For instance: fittest is tautological; adaptable trades off with specialized, so that more adaptable land mammals will often have a slower top speed (flying, running, digging, or swimming); prolific as measured in living young often trades with body size in mammals, so that big litters come from smaller species; survival as measured in lifespan often trades with reproduction as measured in grown young;

so we can reword that for land mammals as follows: the slower, smaller ones with fewer grown young are the more fit. Sound like a good place to start?

 

Individuals change, but that is not the topic of common descent via natural selection. So we usually label an individual's change as "development" as in the growth of a child into an adult.

"Species" is the man-made classification of populations. It is populations, not species and not individuals which change over time. The act of speciation is when either the population forks into more than one distinct populations identifiable by phenotype and there is a barrier to these forks merging together or a variant phenotype arises and is selected for over time replacing the former dominant phenotype which goes extinct. Thus populations change over time and species are names for snapshots of small pieces of the branching tree of life where we can ignore the changes in phenotype.

Individual survival is not the most important factor in evolution. That's because the element of evolution isn't the individual, but the allele -- the various components of the genome. So a brother sacrificing himself for his kin is a viable way for the alleles common to all to survive.

Natural selection doesn't dictate any particular tendency towards prolific reproduction. Both r-type and K-type reproduction strategies are employed by organisms with good effect. https://en.wikipedia.org/wiki/R/K_selection_theory

But in post #22 I attempted to give the OP the mathematical model that he was looking for.