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The More the Merrier?

Entropy and Statistics of Asexual Reproduction in Freshwater Planarians

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An Erratum to this article was published on 11 October 2012

Abstract

The trade-off between traits in life-history strategies has been widely studied for sexual and parthenogenetic organisms, but relatively little is known about the reproduction strategies of asexual animals. Here, we investigate clonal reproduction in the freshwater planarian Schmidtea mediterranea, an important model organism for regeneration and stem cell research. We find that these flatworms adopt a randomized reproduction strategy that comprises both asymmetric binary fission and fragmentation (generation of multiple offspring during a reproduction cycle). Fragmentation in planarians has primarily been regarded as an abnormal behavior in the past; using a large-scale experimental approach, we now show that about one third of the reproduction events in S. mediterranea are fragmentations, implying that fragmentation is part of their normal reproductive behavior. Our analysis further suggests that certain characteristic aspects of the reproduction statistics can be explained in terms of a maximum relative entropy principle.

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References

  1. Agata, K.: Stem cells—from hydra to man. In: Stem Cells in Planarian, pp. 59–74. Springer, Berlin (2008)

    Google Scholar 

  2. Baguna, J., Slack, J.: Planarian neoblasts. Nature 290, 14–15 (1981)

    Article  ADS  Google Scholar 

  3. Baguna, J., Salo, E., Auladell, C.: Regeneration and pattern formation in planarians. III. Evidence that neoblasts are totipotent stem cells and the source of blastema cells. Development 107, 77–86 (1989)

    Google Scholar 

  4. Boyce, M., Perrins, C.: Optimizing great tit clutch size in a fluctuating environment. Ecology 68, 142–153 (1987)

    Article  Google Scholar 

  5. Bronstedt, H.V.: Planarian Regeneration. Pergamon Press, Elmsford (1969)

    Google Scholar 

  6. Calow, P., Beveridge, M., Sibly, R.: Heads and tails: adaptional aspects of asexual reproduction in freshwater triclads. Am. Zool. 19, 715–727 (1979)

    Google Scholar 

  7. Charnov, E., Ernest, S.: The offspring-size/clutch-size trade-off in mammals. Am. Nat. 167(4), 578–582 (2006)

    Article  Google Scholar 

  8. Dunkel, J., Talbot, J., Schötz, E.-M.: Memory and obesity affect the population dynamics of asexual freshwater planarians. Phys. Biol. 8, 026003 (2011)

    Article  ADS  Google Scholar 

  9. Hori, I., Kishida, Y.: A fine structural study of regeneration after fission in the planarian dugesia japonica. Hydrobiologia 383, 131–136 (1998)

    Article  Google Scholar 

  10. Hori, I., Kishida, Y.: Further observation on the early regerates after fission in the planarian dugesia japonica. Belg. J. Zool. 131(Supplement 1), 117–121 (2001)

    Google Scholar 

  11. Jaynes, E.T.: Prior probabilities. IEEE Trans. Syst. Sci. Cybern. 4(3), 227–241 (1968)

    Article  MATH  Google Scholar 

  12. Kawakatsu, M.: An experimental study of the life-history of Japanese freshwater planaria, p. vivida (ijima et kaburaki), with special reference to the fragmentation. Bull Kyoto Gakugei Univ. Ser. B, pp. 35–39 (1959)

  13. Kullback, S., Leibler, RA: On information and sufficiency. Ann. Math. Stat. 22(1), 79–86 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mora, T., Walczak, AM, Bialek, W., Callan, C.G. Jr: Maximum entropy models for antibody diversity. Proc. Natl. Acad. Sci. USA 107, 5405–5410 (2010)

    Article  ADS  Google Scholar 

  15. Newmark, P., Sánchez Alvarado, A.: Not your father’s planarian: a classic model enters the era of functional genomics. Nat. Rev. Genet. 3, 210–220 (2002)

    Article  Google Scholar 

  16. Oviedo, N.J., Levin, M.: Smedinx-11 is a planarian stem cell gap junction gene required for regeneration and homeostasis. Development 134, 3121–3131 (2007)

    Article  Google Scholar 

  17. Peter, R., Ladurner, P., Rieger, R.: The role of stem cell strategies in coping with environmental stress and choosing between alternative reproductive modes: turbellaria rely on a single cell type to maintain individual life and propagate species. Marine. Ecology 22, 35–51 (2001)

    Google Scholar 

  18. Pettifor, RA, Perrins, C.M., McCleery, R.H.: Individual optimization of clutch size in great tits. Nature 336, 160–162 (1988)

    Article  ADS  Google Scholar 

  19. Reddien, P., Sánchez Alvarado, A.: Fundamentals of planarian regeneration. Annu. Rev. Cell Dev. Biol. 20, 725–757 (2004)

    Article  Google Scholar 

  20. Reddien, P., Oviedo, N., Jennings, J., Jenkin, J., Sánchez Alvarado, A.: SMEDWI-2 is a PIWI-like protein that regulates planarian stem cells. Science 310(5752), 1327–1330 (2005)

    Article  ADS  Google Scholar 

  21. Sánchez Alvarado, A., Newmark, P., Robb, S., Juste, R.: The Schmidtea mediterranea database as a molecular resource for studying platyhelminthes, stem cells and regeneration. Development 129, 5659–5665 (2002)

    Article  Google Scholar 

  22. Sheiman, I.M., Sedel’nikov, Z.V., Shkutin, M.F., Kreshchenko, N.D.: Asexual reproduction of planarians: metric studies. Russ. J. Dev. Biol. 37(2), 102–107 (2006)

    Article  Google Scholar 

  23. Sinervo, B., Licht, P.: Proximate constraints on the evolution of egg size, number and total clutch mass in lizards. Science 252, 1300–1302 (1991)

    Article  ADS  Google Scholar 

  24. Sinervo, B., Doughty, P., Huey, R., Zamudio, K.: Allometric engineering: a causal analysis of natural selection on offspring size. Science 258, 1927–1931 (1992)

    Article  ADS  Google Scholar 

  25. Smith, C.C., Fretwell, S.D.: The optimal balance between size and number of offspring. Am. Nat. 108(962), 499–506 (1974)

    Article  Google Scholar 

  26. Smith, H.G., Kallander, H., Nilsson, JA: The trade-off between offspring number and quality in the great tit parus major. J. Anim. Ecol. 58(2), 383–401 (1989)

    Article  Google Scholar 

  27. Stearns, S.: The Evolution of Life Histories. Oxford University Press, London (1992)

    Google Scholar 

  28. Thomas, M., Schötz, E.-M.: SAPling: a scan-add-print barcoding database system to track and label asexual animal colonies, in review (2011)

  29. Visser, M., Verboven, N.: Long-term fitness effects of fledging date in great tits. Oikos 85(3), 445–450 (1999)

    Article  Google Scholar 

  30. Walker, R., Gurven, M., Burger, O., Hamilton, M.: The trade-off between number and size of offspring in humans and other primates. Proc. R. Soc. B 275, 827–834 (2008)

    Article  Google Scholar 

  31. Wehrl, A.: General properties of entropy. Rev. Mod. Phys. 50(2), 221–260 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  32. Zaccanti, F., Farne, P.: Observations on fissiparity and spontaneous regeneration in two strains of agamic planarians (dugesia gonocephala and dugesia tigrina). J. Exp. Zool. 238, 319–324 (1986)

    Article  Google Scholar 

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Correspondence to Eva-Maria Schötz.

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An erratum to this article can be found online at http://dx.doi.org/10.1007/s10955-012-0608-5.

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Quinodoz, S., Thomas, M.A., Dunkel, J. et al. The More the Merrier?. J Stat Phys 142, 1324–1336 (2011). https://doi.org/10.1007/s10955-011-0157-3

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  • DOI: https://doi.org/10.1007/s10955-011-0157-3

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