Chapter 5



This chapter discusses the concept of selection. It is trickier than it may appear at first sight. It is striking that numerous authors in the social sciences use terms such as “variation-selection-retention model” without defining selection or apparently realizing its complexity.

Selection implies an ontology of multiple entities existing at the same point in time. Critics of the selection concept often overlook this. They often regard “evolution” as the process of development of a single entity, which of course is one of several possible meanings of that word. Generalized Darwinism applies to a population of multiple entities.

Selection neither implies progress nor excludes cooperation. It can take different forms and involves multiple possible mechanisms.

Our definition of selection (in section 5.1) follows closely the work of George Price. The definition involves an anterior and posterior set of entities in a population. The posterior set can be a subset of the anterior set (which we call subset selection), or it can be some kind of offspring of the anterior set (which we call successor selection). This definition is helpful for analytical purposes. It can be made operational, and thus useful in empirical research by translation to a regression framework.

Much discussion of selection in the social sciences concentrates simply on subset selection, which in contrast to successor selection, is unable to generate novelty.

The definition of selection involves the tricky concept of fitness: by definition with selection the composition of the posterior set is causally related to fitness. Fitness is easy to define in abstract, mathematical terms. But it is difficult to define its specific expression, in both the biological and the social world. In any case, it does not simply mean survival, thus avoiding a tautological formulation of selection. We see the fitness of an interactor as the propensity of its replicators to replicate, by diffusion to other interactors or by making copies of the interactor.

The objects of selection are interactors. We write of “selection of” such objects. The outcome of the change in the population of interactors is a change in the pool of replicators in the population. This is “selection for”. (The philosopher Elliott Sober introduced the terms “selection of” and “selection for” but we use the distinction in a different way.)

In their 1982 book, Richard Nelson and Sidney Winter describe the introduction or curtailment of routines by management within an organization as selection. In contrast, in our conceptual framework only interactors can be objects of selection. We call the type of process described by Nelson and Winter “replicator manipulation”.

We also define the concept of diffusion in this chapter. Diffusion is a type of inheritance that involves the copying of replicators, but not of interactors. Diffusion is common in the social domain, particularly in regard to ideas and technologies. In these cases, associated habits and routines are copied from one interactor to another.


1. Why does selection not always relate to progress or efficiency, even if it is related to fitness?
2. In what way can a selection process create novelty?
3. Are the difficulties with the fitness concept an insurmountable barrier?
4. What is the relationship between selection and replication?
5. Is diffusion related to fitness?


16 thoughts on “Chapter 5

  1. Stan Salthe

    Your questions:
    1. Why does selection not always relate to progress or efficiency, even if it is related to fitness?
    Because it ‘cannot envision a future.

    2. In what way can a selection process create novelty?
    It does not CREATE anything. Creation comes with ‘mutation’ — now expanded to include self-organizing activities (2009 Visions of Evolution: self-organization proposes what natural selection disposes. Biological Theory 3 (1):17-29. ( David Batten Stan Salthe, Fabio Boschetti)

    3. Are the difficulties with the fitness concept an insurmountable barrier?
    It is difficult to measure actual biological improvement of the organism

    4. What is the relationship between selection and replication?
    Fisher’s Fundamental Theorem of Natural Selection equates them.

    5. Is diffusion related to fitness?
    Anything might relate to fitness

    1. Thorbjørn Knudsen

      Re. 1: I agree!
      Re. 2: Also recombinaton can generate novelty.
      Re. 3: Fitness measures changes in frequencies of various types (e.g. short-armed versus long-armed creatures).
      Re 4: Yes. Also note that there is a straightforward relation between the Price Equation and Fishers Theorem (just abstract from the expectation term in the Price Equation).
      Re. 6: If replication is unrelated to fitness, we have drift, i.e. a random walk in genotypes/ replicators. If diffusion is unrelated to fitness, we have random spread interactors and their associated replicators.

  2. len wallast

    Geoff and Thorbjørn dissect social Darwinian selection in accordance with the many detailed and complicated ways social evolution manifests itself. That we need a social unit of selection (the replicator) to work it out is a necessity. That we base the required selection theory on the three principles of Darwinism is self-evident. That selection is teleological is not only a commonly shared insight, it can also be justified on behalf of Shannon’s existence theorem. In chapter 5 we are reaching less common ground. Nevertheless I am very much concerned with bridging the gap between H&K’s ideas and mine. One unavoidable step is to portray Shannon entropy within the central context of any evolutionary explanation. That is what I miss here. Apart from that, seeming differences between the theory of evolvodynamics and H&K’s approach may be reducible to different ways of expression. For instance it strikes me that H&K’s discernment between subset selection and successor selection reflects the two aspects of selecting I listed in my previous comments: the initial selection of existing input and output from the evolutionary system (In H&K-terminology this might be called anterior selection: it does not change the entropy content of what is selected) and the reduction of entropy input and output by subsequent rearrangement of the order of the selected units of selection (In H&K-terminology this might be called posterior selection: it does change the entropy content of what is selected and so provides for the right formalism of economic and social growth).

    Less happy I am with concepts such as diffusion, clearly introduced to come to grips with the various forms of entropy input, entropy output and entropy transmission flows that go into the different sectors (states, interactors) and that go out of these sectors, such as (in the economic domain) the flows of consumption, investment, wages, depreciation, export, import and the associated entropy transmission flows as they spring from Shannon’s treatment of communication theory. It is here where treatment of the basics of the entropy concept is badly missing. By extending analysis to a multi-sector economy we can deal with all the intersectoral entropy flows that one can think of. Important in this respect is the fundamental law that all evolutionary systems S0 are entropically closed. That is, there are no entropy flows going out or into the overall system (The proof of that law is extremely simple and based on probability considerations). The law answers a lot of our questions.
    I must stress here that we can’t split off the various aspects of Darwinian selection as separately analyzable series of events of selection that each require a different explanation (in terms of parametric postulated equations as found in Price and Nelson & Winter) as H&K appear to suggest. Anterior selection and posterior selection are only two complementary aspects of concurrent inextricable Darwinian principles: selection, variation and inheritance. Another such aspect is input and output selection. This is a topic that remains untreated in H&K’s approach as far as I could figure out. And still another, required to formalize inheritance, is that replicators must have lifetime: a random time at which they originate (their moment of output selection) and another random time at which they expire (their moment of input selection). Moreover selection is always between different states that the outcome of a single draw (unit of selection) of a statistical experiment can be in, but I miss the specification of the states (Note: there must be more than one state) as well as a clear definition of the sample space(s) from or into which is selected as well as a clear cut specification of the time-frame of selection and the related realization of the necessary measures to handle the mind-boggling nonergodicity property of economic and social processes. After all there is only one single unique Shannon- and Darwin-inspired theory of selection that explains all of it together such as input and output selection, teleology, nonergodicity, economic growth, the business cycle, the role of investment in fostering growth, the growth-smothering role of price deflation etcetera. Note: one must always explain within the context of the statistical averages of the ensembles considered.

    It is certainly worthwhile to consider the many diversified aspects of evolutionary selection in detail as H&K do, just to get familiar with the ins and outs of the social evolutionary process. But we should not forget that the evolutionary process eventually produces only dynamically changing statistical averages of entropy stock, entropy flow, entropy growth and entropy circulation rates. This implies e.g. that each unit of selection (each replicator) is a statistical average (one bit of entropy or just a constant number of bits) as well since it must reflect the statistics of the ensemble. That is, the replicator, the beacon of constancy in the course of time, owes its significance to the overall ensemble of population and environment. Its probability (or propensity) of selection does not vary over this ensemble at a particular fixed time because probability is also an average over many draws. Replicators can only differ from one another with respect to the time-instant they have originated and the time-instant they will cease existence. All of this would become clear if we take the trouble to find out what our sample spaces are. Thus I do not share H&K’s idea as worded on page 106 that “diffusion changes social replicators” or that successor selection changes these replicators, unless replicators are no longer conceived as units of selection and will be bereft of their crucial role in the statistical theory of selection. Perhaps H&K are aware of the difficulty involved with claiming the unit of selection to be alterable and manipulable: In the last sentence of page 106 they remark that “replicator manipulation is not selection in the technical sense developed here”. This remark corresponds with their belief “that selection is important in social evolution, but not the only mechanism of change” (See page 90). Does that mean that economic and or social change is partially irreducible to Darwinian selection? However if there were other further unspecified manipulable theories of explanation of social or economic change, what does GD explain? We will only get satisfactory answers if GD offers complete explanations of social and economic change. The simple alternative to avoid the unwelcome conclusion that there are still other theories of explanation needed, is to adopt the evolvodynamics of entropy selection as discussed in my comments on previous chapters. Then we don’t need manipulable replicators.

    The authors close chapter 5 with the suggestion that we can devise a complete system of equations on the basis of approaches employed by Nelson & Winter and the Price-equation. The drawback of following this suggestion is that it results in a system of postulated (not derived) equations of evolutionary variables that are basically parametric. With it we get all the burden of the failures of mainstream economics again on our neck. That is, so called constant parameters are required to implement the system and regression analysis must deliver the parameters that minimize some sort of error-vector or maximize some sort of return. Unfortunately the so called constant parameters turn out always to alter in the course of time. The question that arises then is: what is the significance of the errors we minimize and why does this optimization process at a particular time t deliver a measure of evolutionary fitness F(t)? Clearly, it doesn’t. Each different time t1, t2, t3, …. we repeat the optimization process we get another set of parameters and hence another measure F(t1), F(t2), F(t3),…. of fitness. If we order these fitness outcomes according to magnitude, how then do we know that this is the right order of ordering the fitness of the population in the course of time? We cannot know. As our parameters have changed with time t1, t2, t3, …. ; also our model of the evolutionary process has changed so that we cannot relate one to the other. The outcomes apply to different evolutionary systems because the parameters are different. Taking entropy or complexity as to reflect the measure of fitness will not help to avoid this consequence. One reason is that the parameters will remain changing each different time we repeat the process so that comparison of entropy or complexity measures of fitness will not help either. Another, fundamental, reason is that selection is solely concerned with the reduction of uncertainty. It is definitely not concerned with optimizing fitness, or optimizing entropy or optimizing complexity or minimizing errors (See my comments with respect to previous chapters).
    Thus H&K’s assertion that their solution provides for a non- tautological solution is very much contestable. If we keep embracing the idea that fitness is the measure of evolutionary development, our fate will be that the solution is either inconsistent or tautological. The reduction of uncertainty drives evolution. Fitness does not.
    A final remark. I hope and trust that the critical remarks I made here will not be explained as negative but will be welcomed positively. My ideas proceed from a lifelong mathematical/theoretical interest and involvement with the beta sciences in combination with economics, which solely but scrutinously seeks to avoid the many inconsistency obstacles on the road to GD and to found a truly universal theory of economics that avoids the flaws of mainstream economic theory. The difficulty of this project should not be underestimated. In this regard I consider Geoff’s and Thorbjørn’s book as a milestone towards reaching the above objectives. It needs full attention and support although it has not yet reached the terminal station of this difficult venture. My background is totally different from H&K’s, but the multidisciplinary exchange of ideas is the best and most effective we can do to bridge the gaps and to attain scientific progress.

    1. Thorbjørn Knudsen

      Subset selection is a fundamental process of reducing the number of members in a population according to some criterion. Along the way, the composition of the population may change, and thereby the value of its traits. But as subset selection gradually removes populaton members, it eventually reduces variance. By cntrast, successor selection adds new variance. Successor selection is defined as selection through one cycle of replication, variation, and environmental interaction so structured that the replication process CAUSES new variation (i.e., novel varieties alter the distribution of population properties) and the environmental interaction causes replication to be differential. The Price Equation simply accounts for the change in the first moment (average value) in trait values. It can be used to account for subset selection as well as successor selection. is widely thought to be useful for this purpose. It is a deterministic equation where fitness captures the underlying forces that alter frequencies in the distribution of trait values.

      In chapter 6, we consider the relation between replication and entropy!

  3. koppl

    FWIW, I think the distinction between “subset selection” and “successor selection” if very helpful. Evolutionary processes have an imperfect and reversible tendency toward increasing heterogeneity of populations. Subset selection can’t capture that, because is implies declining heterogeneity. So you must have something more than “selection” if your “evolutionary” argument is going to be analogous to Darwinian evolution in biology. That’s a nice, clean line of argumentation, and I find it helpful.

  4. koppl

    Can you help me to better understand fitness? Fitness is a replicator’s propensity to produce copies. Isn’t it then true by definition that the fittest will have better odds of surviving? We are not defining fitness by survival, it’s true, but it still seems a bit circular to me. I recognize that the problems here apply equally to biological and social evolution. And I don’t think it would necessarily be a problem to say that differential reproductive success for the fitter is part of the Lakatosian hardcore and not subject to *direct* empirical test. But it seemed like you were making a stronger empirical claim in chapter 5.

    1. Geoffrey M Hodgson Post author

      Roger Koppl’s points are important. In part-response there are scenarios where the ability to produce offspring with similar replicators is eventually sub-optimal for survival. In both the social and biological worlds there are frequency and path-dependence effects, for example, that can divert evolution into tracks that restrict or even threaten the survival of the species.

  5. Melissa Dennison

    In evolutionary biology fitness is defined by the number of offspring you leave behind. The greater the number then the more biologically fit you are. As Darwinian theory is a populations based theory then if you leave large numbers of offspring you will have a larger effect on the composition of the population, more individuals in it will have your characteristics. If your offspring are also biologically fit then eventually through selection and the struggle for existence with other unrelated individuals (ie those not sharing your characteristics), then the population comes to look like you. Or shall I say to have your advantageous characteristics. In this way generalized Darwinism is sticking to the initial Darwinian theory I think. So fitness is reproductive success.

    The thing about selection is that it has no goal in sight. Evolutionary theory has often been misunderstood in this respect, as people have assumed that there is an increase in complexity, or a ladder of progress through time from single celled organisms to ourselves. Now on the surface it could look this way, but this is a distorted view of reality. However, interestingly evolution could involve ‘betterment’ as Futuyma (2005) puts it. ie improved learning capacities, or adaptations which suit that particular organism’s requirements. Where social evolution is concerned I would think that diffusion is very important, as ideas and technologies are the things that we see evolving and which influence our evolution in turn. So yes I think this is related to the notion of ‘fitness’. Ideas that are imitated or technologies that are popular could be described in terms of being more fit than those that fall by the wayside or are rare. What do you think?

    1. koppl

      I think your account would make “survival of the fittest” a tautology, Melissa. H&K explicitly deny that it is a tautology. I was questioning how far they have really moved from the strictly tautological version of the idea. Some distance, yes, but how much? At least that’s my best understanding, but I confess to some doubts about what they are saying about this topic.

    2. Geoffrey M Hodgson Post author

      Just a very tiny quibble here. We do not define fitness as the actual number of offspring, but in terms of PROPENSITIES. Bad luck may cause a highly fit individual to be hit by lightning, and and identical individual survives and has lots of offspring. On the second paragraph I agree that selection generally “has no goal on sight”. Artificial selection (such as in pigeon-breeding) may have a goal – but this is a special case. Much of selection in nature and society is a result of undesigned processes.

      1. Melissa Dennison

        If it is undesigned processes then is there room for unpredictability, for chaos and uncertainty? And for the undetermined also? If so then does this contradict Darwinism in some way, as isn’t this deterministic in that scientific laws offer predictability? Bad luck is a random or chance. How does this randomness fit with abstract principles ie selection?

  6. Melissa Dennison

    Hi again, I had another thought that I felt compelled to share. If you are wishing to generalize Darwinism and apply it to society, then why not just say that society is Darwinian? The original theory posited by Charles Darwin was not really a theory consisting of abstract principles that required auxillary theories, it was a theory that was self-contained and sufficient in itself to explain the history of life on this planet. Now granted he did not have the knowledge that we have today, but the basic principles of natural selection, variation, inheritance and the struggle for existence speak for themselves. Just a thought to put out there. Sometimes I wonder if proponents of GD are uncertain as to whether or not they wish to make a comparison between the biological and the social. If you are to apply Darwin’s principles I think there is an acknowledgement here of the connection between the two.

  7. Geoffrey M Hodgson Post author

    We do say that social evolution is Darwinian. We also compare the biological and the social, observing important differences in detail but also establishing communalities at an abstract level. Furthermore, as with Witt’s “continuity hypothesis”, we see connections between the social and the biological world, without reducing one to the other.

  8. Geoffrey M Hodgson Post author

    Melissa asks: “If it is undesigned processes then is there room for unpredictability, for chaos and uncertainty? And for the undetermined also? If so then does this contradict Darwinism in some way, as isn’t this deterministic in that scientific laws offer predictability? Bad luck is a random or chance. How does this randomness fit with abstract principles ie selection?”

    In response, Darwinism definitely involves causal determination (= every event has a cause). But complexity and chaos theory teach us that causal determination does not generally imply predictability. Things can be causally determined but we can be uncertain and unable to predict, especially in complex, non-linear systems. But causal determination contradicts the idea of undetermined (uncaused) events. Furthermore, Darwinism does not necessarily mean randomness. But if outcomes were random or stochastic (as in quantum physics) then this means probabilistic determination, and does not overturn causal determination as formulated in general terms . (See Mario Bunge’s classic book on “Causality”.)

    Generally, Darwinism is more about explanation than prediction. In classical physics, by constrast, there is much more emphasis on prediction. Economists tend to ape physics, rather than biology or other sciences of complexity.

    I hope this helps.

    1. Thorbjørn Knudsen

      A fairly minor addition to the discussion about determinism. The common version of selection mathematics (e.g. as derived from the Price equation) is a deterministic mapping between fitness and change in trait values at the population level. The assumption is that the selection process influences all traits of a similar type in the same way. This assumption could well be lifted, but only at the expense of more involved mathematics. But note that the expected effect of uncertainy, and for that matter complexity, at the level of microprocesses could well be included as sources of fitness, even in the deterministic theory. It is therefore improtant to consider at what level of analysis (micro-, meso-, or macro-scopic), and at what time-scale, uncertainty and chaos wol doccur. Complexity is another kettle of fish, one that we consider in H&K chapter 6.

      1. Geoffrey M Hodgson Post author

        Not disagreeing at all with my co-author, I ought to underline that he is using the word “deterministic” in a mathematical sense. When people discuss “determinism” outside mathematics they generally mean something different, relating to causality, predictability or event regularity. The mathematical meaning is clear and unambiguous (as far as I am aware) but the extra-mathematical usage is plagued with ambiguities.

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