Skip to main content
Log in

Inference algorithms for developmental systems with cell lineages

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

An algorithmic formulation is presented for the inference procedure concerning lineage models. The problem is to find lineage rules from observed sequences of tree structures under the assumption that no interactions take place in the course of development and that sufficiently frequent observations are available at equal time intervals. The underlying structural pattern is taken to be a OL system, and the goal is to find propagating and deterministic OL schemes with minimal properties satifsying certain biological reliance criteria. Upper bounds have been found for the complexity of the inference algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Angluin, D. and C. H. Smith. 1983. “Inductive Inference: Theory and Models.”Comput. Surveys 15, 237–269.

    Article  MathSciNet  Google Scholar 

  • Bell, A. D., D. Roberts and A. Smith. 1979. “Branching Patterns: The Simulation of Plant Architecture.”J. theor. Biol. 81, 351–375.

    Article  Google Scholar 

  • Borchert, R. and H. Honda. 1984. “Control of Development in the Bifurcating Branch System ofTabebuia rosea: A Computer Simulation.”Bot. Gaz. 145, 184–195.

    Article  Google Scholar 

  • Culik, II. K. and D. Wood. 1979. “Doubly Deterministic Tabled OL Systems.”Int. J. Comput. Information Sci. 8, 335–347.

    Article  MATH  MathSciNet  Google Scholar 

  • Eichhorst, P. and W. Savitch. 1980. “Growth Functions of Stochastic Lindenmayer Systems.”Inform. Control 45, 217–228.

    Article  MATH  MathSciNet  Google Scholar 

  • Feliciangeli, H. and G. T. Herman. 1973. “Algorithms for Producing Grammars from Sample Derivations: A Common Problem of Formal Language Theory and Developmental Biology.”J. Comput. Syst. Sci. 7, 97–118.

    MATH  MathSciNet  Google Scholar 

  • Fisher, J. B. and H. Honda. 1979. “Branch Geometry and Effective Leaf Area: A Study of Terminalia Branching Pattern. Part I, II.”Am. J. Bot. 66, 633–644, 645–655.

    Article  Google Scholar 

  • Frijters, D. 1978. “Principles of Simulation of Inflorescence Development. Mechanisms of Developmental Integration ofAster novae-angliae L. andHieracium murorum L.”Ann. Bot. 42, 549–560, 571–575.

    Google Scholar 

  • — and A. Lindenmayer. 1976. “Developmental Descriptions of Branching Patterns with Paracladial Relationships. InAutomata, Languages, Development, A. Lindenmayer and G. Rozenberg. (Eds), pp. 57–73. Amsterdam: North-Holland.

    Google Scholar 

  • Gnutzmann, I. (1979). “Zum syntaktischen Inferenzproblem bei Lindenmayer-Systemen.” Dissertation, Universität of Hannover.

  • Herman, G. T. and G. Rozenberg. 1975.Developmental Systems and Languages. Amsterdam: North-Holland.

    Google Scholar 

  • Herman, G. T. and A. Walker. 1972. “The Syntactic Inference Problem as Applied to Biological Systems.” InMachine Intelligence, Vol. 7, B. Meltzer and D. Michie (Eds), pp. 341–356. Edinburgh: Edinburgh University Press.

    Google Scholar 

  • Jürgensen, H. 1976. “Probabilistic L Systems.” In:Automata, Languages, Development, A. Lindenmayer and G. Rozenberg (Eds), pp. 211–225. Amsterdam: North-Holland.

    Google Scholar 

  • —, D. E. Matthews and D. Wood. 1981. “Life and Death in Markov Deterministic Tabled OL Systems.”Inform. Control 48, 80–93.

    Article  MATH  Google Scholar 

  • Jürgensen, H., D. E. Matthews and D. Wood. (in preparation). “Inference for MDTOL Systems.”

  • Lange, K.-J. 1982. “L Homomorphisms and Reductions of OL Systems.”Int. J. Comput. Math. 11, 197–205.

    MATH  Google Scholar 

  • Lindenmayer, A. 1968. “Mathematical Models for Cellular Interactions in Development. Parts I, II.”J. theor. Biol. 18, 280–299, 300–315.

    Article  Google Scholar 

  • — 1971. “Developmental Systems without Interactions: Their Languages and Grammars.”J. theor. Biol. 30, 455–485.

    Article  Google Scholar 

  • — 1977. “Paracladial Relationships in Leaves.”Ber. Deutsch. Bot. Ges. 90, 287–301.

    Google Scholar 

  • — 1982. “Developmental Algorithms: Lineage versus Interactive Control Mechanisms.” InDevelopmental Order: Its Origin and Regulation (40th Symposium of the Society of Developmental Biology), S. Subtelney and P. B. Green. (Eds), pp. 219–245. New York: Alan R. Liss.

    Google Scholar 

  • — 1984. “Positional and Temporal Control Mechanisms in Inflorescence Development.” InPositional Controls in Plant Development, P. W. Barlow and D. J. Carr (Eds), pp. 461–486. Cambridge: Cambridge University Press.

    Google Scholar 

  • Lück, J. and H. B. Lück. 1982. “Modellbildungen zur pflanzlichen Verzweigung (eine Übersicht).”Ber. Deutsch. Bot. Ges. 95, 75–97.

    Google Scholar 

  • Nishida, T. 1980. “KOL-System Simulating Almost but not Exactly the Same Development.”Mem. Fac. Sci., Kyoto Univ., Ser. Biol. 8, 97–122.

    Google Scholar 

  • Reffye, P. de. 1981. “Modèle mathématique aléatoire et simulation de la croissance et de l'architecture du caféier robusta. I, II.”Café Cacoa Thé 25, 83–104, 219–230.

    Google Scholar 

  • Rozenberg, G. and A. Salomaa. 1980.The Mathematical Theory of L Systems. New York: Academic Press.

    Google Scholar 

  • Schmidt, U. 1983.Syntaktische Inferenz von DTOL-Systemen. Diplomarbeit, Technische Hochschule Darmstadt.

  • Wood, D. 1980.Grammar and L Forms: An Introduction, Lecture Notes in Computer Science, Vol. 91. Berlin: Springer-Verlag.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was supported in part by Grant A0243 of the Natural Sciences and Engineering Research Council of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jürgensen, H., Lindenmayer, A. Inference algorithms for developmental systems with cell lineages. Bltn Mathcal Biology 49, 93–123 (1987). https://doi.org/10.1007/BF02459961

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02459961

Keywords

Navigation