Historical sciences like evolutionary biology reconstruct past events by using the traces that the past has bequeathed to the present. Markov chain theory entails that the passage of time reduces the amount of information that the present provides about the past. Here we use a Moran process framework to show that some evolutionary processes destroy information faster than others. Our results connect with Darwin’s principle that adaptive similarities provide scant evidence of common ancestry whereas neutral and deleterious similarities do better. (...) We also describe how the branching in phylogenetic trees affects the information that the present supplies about the past. (shrink)

Topics in Cognitive Science, Volume 14, Issue 1, Page 163-188, January 2022.

Autocatalytic networks have been used to model the emergence of self‐organizing structure capable of sustaining life and undergoing biological evolution. Here, we model the emergence of cognitive structure capable of undergoing cultural evolution. Mental representations (MRs) of knowledge and experiences play the role of catalytic molecules, and interactions among them (e.g., the forging of new associations) play the role of reactions and result in representational redescription. The approach tags MRs with their source, that is, whether they were acquired through social (...) learning, individual learning (of pre‐existing information), or creative thought (resulting in the generation of new information). This makes it possible to model how cognitive structure emerges and to trace lineages of cumulative culture step by step. We develop a formal representation of the cultural transition from Oldowan to Acheulean tool technology using Reflexively Autocatalytic and Food set generated (RAF) networks. Unlike more primitive Oldowan stone tools, the Acheulean hand axe required not only the capacity to envision and bring into being something that did not yet exist, but hierarchically structured thought and action, and the generation of new MRs: the concepts EDGING, THINNING, SHAPING, and a meta‐concept, HAND AXE. We show how this constituted a key transition toward the emergence of semantic networks that were self‐organizing, self‐sustaining, and autocatalytic, and we discuss how such networks replicated through social interaction. The model provides a promising approach to unraveling one of the greatest anthropological mysteries: that of why development of the Acheulean hand axe was followed by over a million years of cultural stasis. (shrink)

Markov models of evolution describe changes in the probability distribution of the trait values a population might exhibit. In consequence, they also describe how entropy and conditional entropy values evolve, and how the mutual information that characterizes the relation between an earlier and a later moment in a lineage’s history depends on how much time separates them. These models therefore provide an interesting perspective on questions that usually are considered in the foundations of physics—when and why does entropy increase and (...) at what rates do changes in entropy take place? They also throw light on an important epistemological question: are there limits on what your observations of the present can tell you about the evolutionary past? (shrink)

This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We then argue how this has important consequences for the evolvability, enablement, and emergence of autocatalytic sets. We end with some speculation on how all this might lead to a generalized theory of autocatalytic sets, which could possibly be applied to entire ecologies or even (...) economies. (shrink)

We begin by considering two principles, each having the form causal completeness ergo screening-off. The first concerns a common cause of two or more effects; the second describes an intermediate link in a causal chain. They are logically independent of each other, each is independent of Reichenbach's principle of the common cause, and each is a consequence of the causal Markov condition. Simple examples show that causal incompleteness means that screening-off may fail to obtain. We derive a stronger result: in (...) a rather general setting, if the composite cause C1 & C2 & … & Cn screens-off one event from another, then each of the n component causes C1, C2, …, Cn must fail to screen-off. The idea that a cause may be ordinally invariant in its impact on different effects is defined; it plays an important role in establishing this no-go theorem. Along the way, we describe how composite and component causes can all screen-off when ordinal invariance fails. We argue that this theorem is relevant to assessing the plausibility of the two screening-off principles. The discovery of incomplete causes that screen-off is not evidence that causal completeness must engender screening-off. Formal and epistemic analogies between screening-off and determinism are discussed. (shrink)

ABSTRACT Darwin claims in the Origin that similarity is evidence for common ancestry, but that adaptive similarities are ‘almost valueless’ as evidence. This second claim seems reasonable for some adaptive similarities but not for others. Here we clarify and evaluate these and related matters by using the law of likelihood as an analytic tool and by considering mathematical models of three evolutionary processes: directional selection, stabilizing selection, and drift. Our results apply both to Darwin’s theory of evolution and to modern (...) evolutionary biology. _1_ Introduction _2_ The Likelihood Framework _3_ A Sufficient Condition for a Similarity to Favour Common Ancestry over Separate Ancestry _4_ The 1/p Criterion and Its Limitations _5_ Directional Selection versus Drift _6_ Stabilizing Selection versus Drift _7_ Going beyond Two Taxa _8_ Conclusions Appendix. (shrink)

Darwin claims in the Origin that similarity is evidence for common ancestry, but that adaptive similarities are ‘almost valueless’ as evidence. This second claim seems reasonable for some adaptive similarities but not for others. Here we clarify and evaluate these and related matters by using the law of likelihood as an analytic tool and by considering mathematical models of three evolutionary processes: directional selection, stabilizing selection, and drift. Our results apply both to Darwin’s theory of evolution and to modern evolutionary (...) biology. 1 Introduction2 The Likelihood Framework3 A Sufficient Condition for a Similarity to Favour Common Ancestry over Separate Ancestry4 The 1/p Criterion and Its Limitations5 Directional Selection versus Drift6 Stabilizing Selection versus Drift7 Going beyond Two Taxa8 ConclusionsAppendix. (shrink)

The emergence of an autocatalytic network from an available set of elements is a fundamental step in early evolutionary processes, such as the origin of metabolism. Given the set of elements, the reactions between them (chemical or otherwise), and with various elements catalysing certain reactions, a Reflexively Autocatalytic F-generated (RAF) set is a subset R′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document} of reactions that is self-generating from a given food set, and with each reaction in R′\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document} being catalysed from within R′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document}. RAF theory has been applied to various phenomena in theoretical biology, and a key feature of the approach is that it is possible to efficiently identify and classify RAFs within large systems. This is possible because RAFs can be described as the (nonempty) subsets of the reactions that are the fixed points of an (efficiently computable) interior map that operates on subsets of reactions. Although the main generic results concerning RAFs can be derived using just this property, we show that for systems with at least 12 reactions there are generic results concerning RAFs that cannot be proven using the interior operator property alone. (shrink)