Skip to main content
SpringerLink
Log in

On the concept of individual in ecology and evolution

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

Abstract

Part of the art of theory building is to construct effective basic concepts, with a large reach and yet powerful as tools for getting at conclusions. The most basic concept of population biology is that of individual. An appropriately reengineered form of this concept has become the basis for the theories of structured populations and adaptive dynamics. By appropriately delimiting individuals, followed by defining their states as well as their environment, it become possible to construct the general population equations that were introduced and studied by Odo Diekmann and his collaborators. In this essay I argue for taking the properties that led to these successes as the defining characteristics of the concept of individual, delegating the properties classically invoked by philosophers to the secondary role of possible empirical indicators for the presence of those characteristics. The essay starts with putting in place as rule for effective concept engineering that one should go for relations that can be used as basis for deductive structure building rather than for perceived ontological essence. By analysing how we want to use it in the mathematical arguments I then build up a concept of individual, first for use in population dynamical considerations and then for use in evolutionary ones. These two concepts do not coincide, and neither do they on all occasions agree with common intuition-based usage.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ashby WR (1956) Introduction to cybernetics. Chapmann & Hall, London

    MATH  Google Scholar 

  • van Baalen M (2000) The geometry of ecological interactions: simplifying spatial complexity. In: Dieckmann U, Law R, Metz JAJ (eds) Cambridge studies in adaptive dynamics. Cambridge University Press, Cambridge, pp 359–387

  • van Baalen M, Rand DA (1998) The unit of selection in viscous populations and the evolution of altruism. J Theor Biol 193:631–648

    Article  Google Scholar 

  • Bacaër N, Guernaoui S (2006) The epidemic threshold of vector-borne diseases with seasonality: the case of cutaneous leishmaniasis in Chichaoua, Morocco. J Math Biol 53:421–436

    Article  MathSciNet  MATH  Google Scholar 

  • Bacaër N, Ait Dads EH (2012) On the biological interpretation of a definition for the parameter \(R_{0}\) in periodic population models. J Math Biol 65:601–621

    Article  MathSciNet  MATH  Google Scholar 

  • Bocheński IM, Menne A (1965) Grundriss der Logistik. Schöningh, Paderborn

  • Bulmer M (1994) Theor Evol Ecol. Sinauer, Sunderland

    Google Scholar 

  • Cushing JM, Ackleh AS (2011) A net reproductive number for periodic matrix models. J Biol Dyn 6:166–188

    Article  MathSciNet  Google Scholar 

  • Diekmann O (1978) Over Niet–Lineaire Integraalvergelijkingen en Mathematische Epidemiologie. Mathematisch Centrum, Amsterdam

    Google Scholar 

  • Diekmann O (2004) A beginner’s guide to adaptive dynamics. In: Mathematical modelling of population dynamics. Banach Center Publications, vol 63. Institute of Mathematics, Polish Academy of Sciences, Warszawa, pp 47–86

  • Diekmann O, Heesterbeek JAP, Metz JAJ (1990) On the definition and the computation of the basic reproduction ratio \(\text{ R}_{0}\) in models for infectious diseases in heterogeneous populations. J Math Biol 28:365–382

    Article  MathSciNet  MATH  Google Scholar 

  • Diekmann O, Gyllenberg M, Metz JAJ, Thieme HR (1998) On the formulation and analysis of general deterministic structured population models. I. Linear theory. J Math Biol 36:349–388

    Article  MathSciNet  MATH  Google Scholar 

  • Diekmann O, Gyllenberg M, Huang H, Kirkilionis M, Metz JAJ, Thieme HR (2001) On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory. J Math Biol 43:157–189

    Article  MathSciNet  MATH  Google Scholar 

  • Diekmann O, Gyllenberg M, Metz JAJ (2003) Steady state analysis of structured population models. Theor Popul Biol 63:309–338

    Article  MATH  Google Scholar 

  • Diekmann O, Gyllenberg M, Metz JAJ, Nakaoka S, de Roos AM (2010) Daphnia revisited: local stability and bifurcation theory for physiologically structured population models explained by way of an example. J Math Biol 61:277–318

    Article  MathSciNet  MATH  Google Scholar 

  • Durinx M, Metz JAJ, Meszéna G (2008) Adaptive dynamics for physiologically structured models. J Math Biol 56:673–742. doi:10.1007/s00285-007-0134-2

    Article  MathSciNet  MATH  Google Scholar 

  • Feller W (1950) An introduction to probability theory and its applications. Wiley, New York

    MATH  Google Scholar 

  • Geritz SAH, Kisdi É, Meszéna G, Metz JAJ (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol Ecol 12:35–57

    Article  Google Scholar 

  • Gyllenberg M, Metz JAJ (2001) On fitness in structured metapopulations. J Math Biol 43:545–560

    Article  MathSciNet  MATH  Google Scholar 

  • Gyllenberg M, Metz JAJ, Service R (2011) When do optimisation arguments make evolutionary sense? In: Chalub FACC, Rodrigues JF (eds) The mathematics of Darwin’s legacy. Birkhauser, Basel

  • Jagers P (1975) Branching processes with biological applications. Wiley, London

    MATH  Google Scholar 

  • Kalman RE, Falb PL, Arbib MA (1969) Topics in mathematical system theory. McGraw-Hill, New York

    MATH  Google Scholar 

  • Lion S, van Baalen M (2009) The evolution of juvenile–adult interactions in populations structured in age and space. Theor Popul Biol 76:132–145

    Article  MATH  Google Scholar 

  • Matsuda H, Ogita N, Sasaki A, Sato K (1992) Statistical mechanics of population. Prog Theor Phys 88:1035–1049

    Article  Google Scholar 

  • Metz JAJ (2008) Fitness. In: Jørgensen SE, Fath BD (eds) Evolutionary ecology encyclopedia of ecology, vol 2. Elsevier, Oxford, pp 1599–1612

    Chapter  Google Scholar 

  • Metz JAJ (2011) Thoughts on the geometry of meso-evolution: collecting mathematical elements for a post-modern synthesis. In: Chalub FACC, Rodrigues JF (eds) The mathematics of Darwin’s legacy. Birkhauser, Basel, pp 197–234

    Google Scholar 

  • Metz JAJ (2012) Adaptive dynamics. In: Hastings A, Gross LJ (eds) Encyclopedia of theoretical ecology. California University Press, California

    Google Scholar 

  • Metz JAJ, Diekmann O (1986) The dynamics of physiologically structured populations. Lecture notes in biomathematics, vol 68. Springer, Berlin

    Google Scholar 

  • Metz JAJ, Gyllenberg M (2001) How should we define fitness in structured metapopulation models? Including an application to the calculation of ES dispersal strategies. Proc Roy Soc B 268:499–508

    Article  Google Scholar 

  • Metz JAJ, Leimar O (2011) A simple fitness proxy for ESS calculations in structured populations with continuous traits, with applications to the evolution of haplo-diploids and genetic dimorphisms. J Biol Dyn 5:163–190

    Article  MathSciNet  Google Scholar 

  • Metz JAJ, de Roos AM (1992) The role of physiologically structured population models within a general individual-based modeling perspective. In: DeAngelis DL, Gross LJ (eds) Individual-based models and approaches in ecology. Chapman & Hall, Routledge, pp 88–111

    Google Scholar 

  • Metz JAJ, Nisbet RM, Geritz SAH (1992) How should we define “fitness” for general ecological scenarios? TREE 7:198–202

    Google Scholar 

  • Metz JAJ, Geritz SAH, Meszéna G, Jacobs FJA, van Heerwaarden JS (1996) Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In: van Strien SJ, Verduijn Lunel SM (eds) Stochastic and spatial structures of dynamical systems. A’dam, North-Holland, pp 183–231

    Google Scholar 

  • Metz JAJ, Mollison D, van den Bosch F (2000) The dynamics of invasion waves. In: Dieckmann U, Law R, Metz JAJ (eds) The geometry of ecological interactions: simplifying spatial complexity. Cambridge University Press, Cambridge, pp 482–512

  • Metz JAJ, Mylius SD, Diekmann O (2008) When does evolution optimise? Evol Ecol Res 10:629–654

    Google Scholar 

  • Parvinen K, Metz JAJ (2008) On diploid versus clonal ESSes in metapopulations. Theor Pop Biol 73:517–528

    Article  MATH  Google Scholar 

  • Rueffler C, Metz JAJ (2012) Necessary and sufficient conditions for \(R_{0}\) to be a sum of contributions of fertility loops. J Math Biol. doi:10.1007/s00285-012-0603-0

  • Russell B (1940) An inquiry into meaning and truth. Allen& Unwin, London

    Google Scholar 

  • Shaw AK, Levin SA (2012) The evolution of intermittent breeding. J Math Biol. doi:10.1007/s00285-012-0603-0

  • Steiner H-G (1964) Mengen, Abbildungen und Strukturen. In: Behnke H, Remmert R, Steiner H-G, Tietz H (eds) Das Fisher Lexicon Mathematik, vol I. Fisher Bücherei, Frankfurt am Main, pp 246–292

    Google Scholar 

  • Woodger JH (1937) The axiomatic method in biology. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Woodger JH (1939) The technique of theory construction. University of Chicago Press, Chicago

    Google Scholar 

  • Woodger JH (1952) Biology and language. Cambridge University Press, Cambridge

    Google Scholar 

  • Zadeh LA, Desoer CA (1963) Linear systems theory, the state space approach. McGraw-Hill, New York

    Google Scholar 

Download references

Acknowledgments

The present note got of the ground in a workshop on Evolutionary and Ecological Individuals, organised by Philippe Huneman and Minus van Baalen in the context of the multidisciplinary project Ecology and Philosophy: Individuality, Stability & Ethics, funded by the research program “Ingénierie Ecologique” of the CNRS Institut National Ecologie et Environnement. This work benefitted from the support from the “Chaire Modélelisation Mathématique et Biodiversité of Veolia Environnement- Ecole Polytechnique - Museum National d’Histoire Naturelle - Fondation X”.

Author information

Authors and Affiliations

  1. Institute of Biology and Mathematical Institute & NCB, Naturalis, Leiden, The Netherlands

    J. A. J. Metz

  2. Evolution and Ecology Program, IIASA, Laxenburg, Austria

    J. A. J. Metz

Authors
  1. J. A. J. Metz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. A. J. Metz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Metz, J.A.J. On the concept of individual in ecology and evolution. J. Math. Biol. 66, 635–647 (2013). https://doi.org/10.1007/s00285-012-0610-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-012-0610-1

Keywords

Mathematics Subject Classification (2010)

Search

Navigation