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.

  • $\begingroup$ This question is quite wide i hope you will get answer. $\endgroup$ – L.Diago May 27 '18 at 8:35
  • $\begingroup$ @L.Diago, but someone could give me SOME suggestion, without necessarily giving me everything I’m interested in, right? $\endgroup$ – user56834 May 27 '18 at 8:40
  • $\begingroup$ [Thomas Cavier-Smith] (en.wikipedia.org/wiki/Thomas_Cavalier-Smith) had interesting idea about inheritance in clay. But this theory have never been proved/ disproved (some guy tried to do something like that but not with clay). I am not quite sure how the influence selection would look like. But if non-random mutation exist i thing the specious wont be able to adapt to their $\endgroup$ – L.Diago May 27 '18 at 8:55
  • $\begingroup$ enviroment effectlivly on the other hand you technicly can be a X-man in world of non random mutation. So in our world all mutation is random but there is some region which can be more mutated then others part of DNA. Others non biological evolution system is for example you languages systems. I hope i tell you something what do you really want to. $\endgroup$ – L.Diago May 27 '18 at 8:55
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    $\begingroup$ @L.diago, note that non-random mutation doesnt mean NO mutation. It just means that there is some directionality to the mutation. For example, I've heard it argued that businesses evolve according to a kind of non-random mutation. But yes language evolution s another example! I would like a book on the formal properties of such evolutionary systems. If there is no such book, any book that is somewhat like it would be welcome as well! $\endgroup$ – user56834 May 27 '18 at 11:41

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.

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    $\begingroup$ Summarizing evolutionary processes to game theory is, IMO, border-line ridicule. Of course evolution of social behaviour do matter but in no way can evolutionary game theory be seen as the core principle of any thin one would want to call evolution. Typically, I don't think game theory is being used in evolutionary algorithm at all. $\endgroup$ – Remi.b Jun 1 '18 at 14:17
  • $\begingroup$ Evolutionary game theory applies to any and all evolutionary processes. It is not tied to social behavior in any interesting sense. $\endgroup$ – Schiphol Jun 1 '18 at 16:07
  • $\begingroup$ From wikipedia : Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers". Its application to evolutionary processes as well as Hamilton's extension by including a relatedness term are fundamentally limited to the study of the evolution of interactions (conflict, cooperation, etc..) among agents (aka. social evolution). $\endgroup$ – Remi.b Jun 1 '18 at 16:18
  • $\begingroup$ Evolutionary game theory precisely forgoes the assumption of rationality in favor of evolutionary regimes. The interactions and conflicts in EGT usually just codify differences in fitness between, e.g., a base phenotype and a mutant. $\endgroup$ – Schiphol Jun 1 '18 at 20:09

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).

  • $\begingroup$ see my answer, I'm guessing those parts that are less clear come from fusing ideas on natural selection, Hardy-Weinberg population stuff, and neutral theory. In which case I think the related monographs should clear it up. Just throw up your favourite evolution books! I would love to hear them as well. $\endgroup$ – NatWH May 27 '18 at 15:55
  • $\begingroup$ "by 'random change' I suppose you mean genetic drift but I am not sure." No I simply mean mutation of individual genes. "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." No that is not the reason why I mention it. I mention it because I am specifically interested in the process of evolution in general, not just to organisms. $\endgroup$ – user56834 May 27 '18 at 16:08
  • $\begingroup$ By "evolution" I mean the general process that occurs roughly whereby (1) there is a sequence of "samples" from a space of possible elements (e.g. a sample from the space of possible DNA sequences, where each such sample is a "generation" of individuals), and where each sample is determined as a random deviation from the previous sample (previous generation). $\endgroup$ – user56834 May 27 '18 at 16:11
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    $\begingroup$ @NatWH I've listed books I like in the linked post Books on population or evolutionary genetics?. My worry with suggesting a book like The Neutral Theory of Molecular Evolution is that it is not introductory and the OP might have a hard time reading it. I have never read Gould and Lewontin so I can't comment on these books. $\endgroup$ – Remi.b May 27 '18 at 16:11
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    $\begingroup$ Of course, they exist. The book I suggested (as well as Kimura's book NatWH suggested) are all about modelling. There is no mention of specific species. It will teach you how to compute expected heterozygosity after n generations of drift and selection and other stuff of the kind. Generally speaking, there is a lot of math in evolutionary biology, more than in most other fields of biology. $\endgroup$ – Remi.b May 27 '18 at 16:46

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.

  • $\begingroup$ Add in several of Dawkins books (selfish gene, extended phenotype, and climbing mount improbable) which will dive into basic assumptions, artificial evolution and provide a counterpoint to Gould. $\endgroup$ – John May 27 '18 at 17:08
  • $\begingroup$ @John I would classify most of those under things OP would already have read, given the intro to his question. Dawkins is one of the most well-known popular science authors after all. Also bringing in some Dawkins necessitates bringing in some E. O. Wilson... $\endgroup$ – NatWH May 27 '18 at 17:14
  • $\begingroup$ I make no assumptions about what the OP has read since they seem unclear about some of the basic tenets of evolution. And of course asking about non-biological evolution always makes me think of dawkins work on virtual/simulated evolution and ideas about memetics. $\endgroup$ – John May 27 '18 at 17:20
  • $\begingroup$ Eh, I've voted it be closed, anyway. You're right that it is far too vague, and appears to be more about machine learning. $\endgroup$ – NatWH May 27 '18 at 17:22
  • $\begingroup$ @John, purely out of curiosity: what basic tenets do I seem unclear about? $\endgroup$ – user56834 May 27 '18 at 18:02

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