(Reference request) Formal abstract theory of evolution?

EDIT: please feel free to suggest books that are the closest you can come up with to what I'm looking for, even if it doesn't exactly overlap!

I am very well acquainted with the theory of evolution as informally taught. E.g. I don't need a book that explains the theory, or refutes popular misconceptions.

Instead, I am looking for a formal theory of evolution as a process, and I am not specifically interested in the biological aspect of evolution, but in evolution as a more generally occuring process.

  • How do we formally state the different assumptions of Darwinian evolution? (Random change, heritability, natural selection).
  • What happens if we change these different assumptions? (Non-random mutation? Maybe, selection criteria that are influenced by the mutations, rather than independent of it)
  • Are there quantitatively different results of evolution based on these assumptions?
  • Something I find very interesting: What kind of non-biological evolutionary processes can we describe formally? E.g. evolution based on some form of non-random mutation, or based on different types of heritability. What are the different implications of different formal assumptions. How do these differences apply to different evolutionary systems? (E.g. evolution of ideas, cultures, computer viruses, evolutionary algorithms).

In summary, I am looking for a book that introduces in a very abstract way the properties of evolutionary systems (does not have to be focused on biological evolution. I'm interested in the formal properties of such systems).

NOTE: I am NOT asking about a book on modelling highly specific processes that apply to specific biological systems, such as population dynamics of preditor-prey relations. I'm interested in general, abstract theoretical analysis of the notion of an evolutionary process in general.

The theoretical framework that best fits the kinds of questions you have in mind is evolutionary game theory.

The foundational text is perhaps Maynard Smith's Evolution and the Theory of Games, but I'd recommend one of the standard textbooks instead, say Gintis (2000), Game Theory Evolving or the more advanced Hofbauer and Sigmund (1998), Evolutionary Games and Population Dynamics.

Difficulties in your question

It is a little hard to know exactly what you're after because 1) the question is broad 2) some concepts you talk about are a bit unclear.

For example, by 'random change' I suppose you mean genetic drift but I am not sure. The term 'random mutation' is a little undefined (see this post). You list 'Random change, heritability, natural selection' as a list of assumptions (at least I think you mean those are assumptions) but those are typically not common assumptions of evolutionary models. Also, the list is not in any way intuitive, so it is unclear what you mean by it. The phrasing "selection criteria that are influenced by the mutations" is also very unclear. Of course, selection, by definition, is dependent upon the genetic variance.

From our discussion in the comments, I think you are attempting to group different fields under a single concept just because they have the same name. But it is not because they have the same name that they are governed by the same basic principles. For example, it is not because the concept of plasticity exists in both biology and physics that these concepts are in any way related and that there is a general theory of plasticity that encompass both fields.

Evolutionary genetics

That being said, you could gain from any good intro textbook to evolutionary genetics. I especially recommend Population genetics, a concise guide. You will find more such recommendation in the post Books on population or evolutionary genetics?.

Evolution of ideas, cultures, computer viruses, evolutionary algorithms

In your last question you mention 'evolution of ideas, cultures, computer viruses, evolutionary algorithms'. I think you are referring to these concepts so as to clarify that you are not so much interested in the biology of specific organisms but really into the process of evolution. I do not recommend starting reading about these concepts before having a background in evolutionary genetics. You might otherwise make the mistake to over stretch an analogy.

Note also that the field of memetics (evolution of ideas, cultures) is a young field in which very little empirical testing is possible. So, I don't think it is wise to start there if your goal is to increase your understanding of evolutionary biology.

In any case, I am not able to suggest a good book in any of these fields (Evolution of ideas, cultures, computer viruses, evolutionary algorithms).

As a body of literature, that covers quite a broad range of topics that have been discussed at length in many, many papers. Of course, you might find something out of a broad-level textbook (I suggest Futuyma's Evolution). You might also enjoy Kimura's The Neutral Theory of Molecular Evolution (although be aware of its follow ups and critics), and its (somewhat) ecological counterpart, Hubbell's The Unified Neutral Theory of Biodiversity and Biogeography. There are loads more, but this might be a good starting point.

EDIT: also Gould's The Structure of Evolutionary Theory, and Lewontin's The Genetic Basis of Evolutionary Change.

EDIT: also, not directly but since I have just finished reading it: Simpson's Tempo and Mode in Evolution. This is mostly from a palaeontology perspective, but it brilliantly preempts several arguments about rates of phenotypic evolution, individual vs population processes, and the asymmetry between mutation and substitution and what that means for evolutionary biology.