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Chakraborty S, Chakraborty S. Selection-recombination-mutation dynamics: Gradient, limit cycle, and closed invariant curve. Phys Rev E 2023; 108:064404. [PMID: 38243506 DOI: 10.1103/physreve.108.064404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 11/07/2023] [Indexed: 01/21/2024]
Abstract
In this paper, the replicator dynamics of the two-locus two-allele system under weak mutation and weak selection is investigated in a generation-wise nonoverlapping unstructured population of individuals mating at random. Our main finding is that the dynamics is gradient-like when the point mutations at the two loci are independent. This is in stark contrast to the case of one-locus-multi-allele where the existence gradient behavior is contingent on a specific relationship between the mutation rates. When the mutations are not independent in the two-locus-two-allele system, there is the possibility of nonconvergent outcomes, like asymptotically stable oscillations, through either the Hopf bifurcation or the Neimark-Sacker bifurcation depending on the strength of the weak selection. The results can be straightforwardly extended for multilocus-two-allele systems.
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Affiliation(s)
- Suman Chakraborty
- Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
| | - Sagar Chakraborty
- Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
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2
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Levin M. Darwin's agential materials: evolutionary implications of multiscale competency in developmental biology. Cell Mol Life Sci 2023; 80:142. [PMID: 37156924 PMCID: PMC10167196 DOI: 10.1007/s00018-023-04790-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2023] [Revised: 04/24/2023] [Accepted: 04/27/2023] [Indexed: 05/10/2023]
Abstract
A critical aspect of evolution is the layer of developmental physiology that operates between the genotype and the anatomical phenotype. While much work has addressed the evolution of developmental mechanisms and the evolvability of specific genetic architectures with emergent complexity, one aspect has not been sufficiently explored: the implications of morphogenetic problem-solving competencies for the evolutionary process itself. The cells that evolution works with are not passive components: rather, they have numerous capabilities for behavior because they derive from ancestral unicellular organisms with rich repertoires. In multicellular organisms, these capabilities must be tamed, and can be exploited, by the evolutionary process. Specifically, biological structures have a multiscale competency architecture where cells, tissues, and organs exhibit regulative plasticity-the ability to adjust to perturbations such as external injury or internal modifications and still accomplish specific adaptive tasks across metabolic, transcriptional, physiological, and anatomical problem spaces. Here, I review examples illustrating how physiological circuits guiding cellular collective behavior impart computational properties to the agential material that serves as substrate for the evolutionary process. I then explore the ways in which the collective intelligence of cells during morphogenesis affect evolution, providing a new perspective on the evolutionary search process. This key feature of the physiological software of life helps explain the remarkable speed and robustness of biological evolution, and sheds new light on the relationship between genomes and functional anatomical phenotypes.
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Affiliation(s)
- Michael Levin
- Allen Discovery Center at Tufts University, 200 Boston Ave. 334 Research East, Medford, MA, 02155, USA.
- Wyss Institute for Biologically Inspired Engineering at Harvard University, 3 Blackfan St., Boston, MA, 02115, USA.
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Czégel D, Giaffar H, Csillag M, Futó B, Szathmáry E. Novelty and imitation within the brain: a Darwinian neurodynamic approach to combinatorial problems. Sci Rep 2021; 11:12513. [PMID: 34131159 PMCID: PMC8206098 DOI: 10.1038/s41598-021-91489-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 05/21/2021] [Indexed: 02/05/2023] Open
Abstract
Efficient search in vast combinatorial spaces, such as those of possible action sequences, linguistic structures, or causal explanations, is an essential component of intelligence. Is there any computational domain that is flexible enough to provide solutions to such diverse problems and can be robustly implemented over neural substrates? Based on previous accounts, we propose that a Darwinian process, operating over sequential cycles of imperfect copying and selection of neural informational patterns, is a promising candidate. Here we implement imperfect information copying through one reservoir computing unit teaching another. Teacher and learner roles are assigned dynamically based on evaluation of the readout signal. We demonstrate that the emerging Darwinian population of readout activity patterns is capable of maintaining and continually improving upon existing solutions over rugged combinatorial reward landscapes. We also demonstrate the existence of a sharp error threshold, a neural noise level beyond which information accumulated by an evolutionary process cannot be maintained. We introduce a novel analysis method, neural phylogenies, that displays the unfolding of the neural-evolutionary process.
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Affiliation(s)
- Dániel Czégel
- Institute of Evolution, Centre for Ecological Research, Budapest, Hungary.
- Department of Plant Systematics, Ecology and Theoretical Biology, Eötvös University, Budapest, Hungary.
- Parmenides Foundation, Center for the Conceptual Foundations of Science, Pullach, Germany.
- Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ, USA.
| | - Hamza Giaffar
- Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, USA
| | - Márton Csillag
- Institute of Evolution, Centre for Ecological Research, Budapest, Hungary
| | - Bálint Futó
- Institute of Evolution, Centre for Ecological Research, Budapest, Hungary
| | - Eörs Szathmáry
- Institute of Evolution, Centre for Ecological Research, Budapest, Hungary.
- Department of Plant Systematics, Ecology and Theoretical Biology, Eötvös University, Budapest, Hungary.
- Parmenides Foundation, Center for the Conceptual Foundations of Science, Pullach, Germany.
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Stulp F, Oudeyer PY. Proximodistal exploration in motor learning as an emergent property of optimization. Dev Sci 2017; 21:e12638. [PMID: 29285864 DOI: 10.1111/desc.12638] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Accepted: 07/18/2017] [Indexed: 11/27/2022]
Abstract
To harness the complexity of their high-dimensional bodies during sensorimotor development, infants are guided by patterns of freezing and freeing of degrees of freedom. For instance, when learning to reach, infants free the degrees of freedom in their arm proximodistally, that is, from joints that are closer to the body to those that are more distant. Here, we formulate and study computationally the hypothesis that such patterns can emerge spontaneously as the result of a family of stochastic optimization processes, without an innate encoding of a maturational schedule. In particular, we present simulated experiments with an arm where a computational learner progressively acquires reaching skills through adaptive exploration, and we show that a proximodistal organization appears spontaneously, which we denote PDFF (Proximo Distal Freezing and Freeing of degrees of freedom). We also compare this emergent organization between different arm morphologies-from human-like to quite unnatural ones-to study the effect of different kinematic structures on the emergence of PDFF.
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Affiliation(s)
- Freek Stulp
- FLOWERS Team, INRIA Bordeaux Sud-Ouest, Talence, France.,ENSTA ParisTech, Université Paris-Saclay, Paris, France.,German Aerospace Center (DLR), Institute of Robotics and Mechatronics, Wessling, Germany
| | - Pierre-Yves Oudeyer
- FLOWERS Team, INRIA Bordeaux Sud-Ouest, Talence, France.,ENSTA ParisTech, Université Paris-Saclay, Paris, France
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Szilágyi A, Zachar I, Fedor A, de Vladar HP, Szathmáry E. Breeding novel solutions in the brain: a model of Darwinian neurodynamics. F1000Res 2016; 5:2416. [PMID: 27990266 PMCID: PMC5130073 DOI: 10.12688/f1000research.9630.2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 06/21/2017] [Indexed: 01/03/2023] Open
Abstract
Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods: We combine known components of the brain – recurrent neural networks (acting as attractors), the action selection loop and implicit working memory – to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns) with hereditary variation and novel variants appear due to (i) noisy recall of patterns from the attractor networks, (ii) noise during transmission of candidate solutions as messages between networks, and, (iii) spontaneously generated, untrained patterns in spurious attractors. Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection) and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.
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Affiliation(s)
- András Szilágyi
- MTA-ELTE Theoretical Biology and Evolutionary Ecology Research Group, Budapest, H-1117, Hungary.,Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary
| | - István Zachar
- Department of Plant Systematics, Ecology and Theoretical Biology, Institute of Biology, Eötvös University, Budapest, H-1117, Hungary.,Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary
| | - Anna Fedor
- MTA-ELTE Theoretical Biology and Evolutionary Ecology Research Group, Budapest, H-1117, Hungary.,Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary
| | - Harold P de Vladar
- Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary
| | - Eörs Szathmáry
- MTA-ELTE Theoretical Biology and Evolutionary Ecology Research Group, Budapest, H-1117, Hungary.,Department of Plant Systematics, Ecology and Theoretical Biology, Institute of Biology, Eötvös University, Budapest, H-1117, Hungary.,Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary.,Evolutionary Systems Research Group, MTA Ecological Research Centre, Tihany, Hungary
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Szilágyi A, Zachar I, Fedor A, de Vladar HP, Szathmáry E. Breeding novel solutions in the brain: a model of Darwinian neurodynamics. F1000Res 2016; 5:2416. [PMID: 27990266 DOI: 10.12688/f1000research.9630.1] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 09/20/2016] [Indexed: 01/15/2023] Open
Abstract
Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods: We combine known components of the brain - recurrent neural networks (acting as attractors), the action selection loop and implicit working memory - to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns) with hereditary variation and novel variants appear due to (i) noisy recall of patterns from the attractor networks, (ii) noise during transmission of candidate solutions as messages between networks, and, (iii) spontaneously generated, untrained patterns in spurious attractors. Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection) and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.
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Affiliation(s)
- András Szilágyi
- MTA-ELTE Theoretical Biology and Evolutionary Ecology Research Group, Budapest, H-1117, Hungary.,Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary
| | - István Zachar
- Department of Plant Systematics, Ecology and Theoretical Biology, Institute of Biology, Eötvös University, Budapest, H-1117, Hungary.,Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary
| | - Anna Fedor
- MTA-ELTE Theoretical Biology and Evolutionary Ecology Research Group, Budapest, H-1117, Hungary.,Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary
| | - Harold P de Vladar
- Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary
| | - Eörs Szathmáry
- MTA-ELTE Theoretical Biology and Evolutionary Ecology Research Group, Budapest, H-1117, Hungary.,Department of Plant Systematics, Ecology and Theoretical Biology, Institute of Biology, Eötvös University, Budapest, H-1117, Hungary.,Parmenides Center for the Conceptual Foundations of Science, Munich/Pullach, 82049, Germany.,Institute of Advanced Studies, Kőszeg, H-9730, Hungary.,Evolutionary Systems Research Group, MTA Ecological Research Centre, Tihany, Hungary
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Abstract
Standard evolutionary dynamics is limited by the constraints of the genetic system. A central message of evolutionary neurodynamics is that evolutionary dynamics in the brain can happen in a neuronal niche in real time, despite the fact that neurons do not reproduce. We show that Hebbian learning and structural synaptic plasticity broaden the capacity for informational replication and guided variability provided a neuronally plausible mechanism of replication is in place. The synergy between learning and selection is more efficient than the equivalent search by mutation selection. We also consider asymmetric landscapes and show that the learning weights become correlated with the fitness gradient. That is, the neuronal complexes learn the local properties of the fitness landscape, resulting in the generation of variability directed towards the direction of fitness increase, as if mutations in a genetic pool were drawn such that they would increase reproductive success. Evolution might thus be more efficient within evolved brains than among organisms out in the wild.
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Affiliation(s)
- Harold P de Vladar
- Center for the Conceptual Foundations of Science , Parmenides Foundation , Kirchplatz 1, Pullach 82049 , Germany
| | - Eörs Szathmáry
- Center for the Conceptual Foundations of Science , Parmenides Foundation , Kirchplatz 1, Pullach 82049 , Germany ; Institute of Biology , Eötvös University , Pázmány Péter sétány 1/C, Budapest 1117 , Hungary ; TMTA-ELTE Theoretical Biology and Evolutionary Ecology Research Group , Pázmány Péter sétány 1/C, Budapest 1117 , Hungary
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8
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Fernando C. From Blickets to Synapses: Inferring Temporal Causal Networks by Observation. Cogn Sci 2013; 37:1426-70. [DOI: 10.1111/cogs.12073] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2012] [Revised: 09/12/2012] [Accepted: 12/17/2012] [Indexed: 01/08/2023]
Affiliation(s)
- Chrisantha Fernando
- School of Electrical Engineering and Computer Science; Queen Mary University of London
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Fernando C, Szathmáry E, Husbands P. Selectionist and evolutionary approaches to brain function: a critical appraisal. Front Comput Neurosci 2012; 6:24. [PMID: 22557963 PMCID: PMC3337445 DOI: 10.3389/fncom.2012.00024] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2011] [Accepted: 04/05/2012] [Indexed: 01/05/2023] Open
Abstract
We consider approaches to brain dynamics and function that have been claimed to be Darwinian. These include Edelman’s theory of neuronal group selection, Changeux’s theory of synaptic selection and selective stabilization of pre-representations, Seung’s Darwinian synapse, Loewenstein’s synaptic melioration, Adam’s selfish synapse, and Calvin’s replicating activity patterns. Except for the last two, the proposed mechanisms are selectionist but not truly Darwinian, because no replicators with information transfer to copies and hereditary variation can be identified in them. All of them fit, however, a generalized selectionist framework conforming to the picture of Price’s covariance formulation, which deliberately was not specific even to selection in biology, and therefore does not imply an algorithmic picture of biological evolution. Bayesian models and reinforcement learning are formally in agreement with selection dynamics. A classification of search algorithms is shown to include Darwinian replicators (evolutionary units with multiplication, heredity, and variability) as the most powerful mechanism for search in a sparsely occupied search space. Examples are given of cases where parallel competitive search with information transfer among the units is more efficient than search without information transfer between units. Finally, we review our recent attempts to construct and analyze simple models of true Darwinian evolutionary units in the brain in terms of connectivity and activity copying of neuronal groups. Although none of the proposed neuronal replicators include miraculous mechanisms, their identification remains a challenge but also a great promise.
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Affiliation(s)
- Chrisantha Fernando
- School of Electronic Engineering and Computer Science, Queen Mary, University of London London, UK
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