Bulletin of Mathematical Biology

, Volume 81, Issue 3, pp 878–898 | Cite as

The Species Problem from the Modeler’s Point of View

  • Marc Manceau
  • Amaury LambertEmail author


How to define a partition of individuals into species is a long-standing question called the species problem in systematics. Here, we focus on this problem in the thought experiment where individuals reproduce clonally and both the differentiation process and the population genealogies are explicitly known. We specify three desirable properties of species partitions: (A) Heterotypy between species, (B) Homotypy within species and (M) Genealogical monophyly of each species. We then ask: How and when is it possible to delineate species in a way satisfying these properties? We point out that the three desirable properties cannot in general be satisfied simultaneously, but that any two of them can. We mathematically prove the existence of the finest partition satisfying (A) and (M) and the coarsest partition satisfying (B) and (M). For each of them, we propose a simple algorithm to build the associated phylogeny out of the genealogy. The ways we propose to phrase the species problem shed new light on the interaction between the genealogical and phylogenetic scales in modeling work. The two definitions centered on the monophyly property can readily be used at a higher taxonomic level as well, e.g., to cluster species into monophyletic genera.


Genealogy Phylogeny Microevolution Macro-evolution Individual-based model Species concept 



The authors are very grateful to F. Débarre, R.S. Etienne, M. Steel, S. Türpitz and A. Hoppe for their comments on this paper, and to D. Baum for helpful literature advice. The authors thank the Center for Interdisciplinary Research in Biology (CIRB, Collège de France) for funding, as well as the École Normale Supérieure for MM PhD funding. We declare no conflict of interest.


  1. Aguilée R, Lambert A, Claessen D (2011) Ecological speciation in dynamic landscapes. J Evol Biol 24:2663–2677Google Scholar
  2. Aldous D, Krikun M, Popovic L (2008) Stochastic models for phylogenetic trees on higher-order taxa. J Math Biol 56:525–557MathSciNetzbMATHGoogle Scholar
  3. Aldous DJ, Krikun MA, Popovic L (2011) Five statistical questions about the tree of life. Syst Biol 60:318–328Google Scholar
  4. Alexander SA (2013) Infinite graphs in systematic biology, with an application to the species problem. Acta Biotheor 61:181–201Google Scholar
  5. Alexander SA, de Bruin A, Kornet DJ (2015) An alternative construction of internodons: the emergence of a multi-level tree of life. Bull Math Biol 77:23–45MathSciNetzbMATHGoogle Scholar
  6. Avise JC, Ball RM (1990) Principles of genealogical concordance in species concepts and biological taxonomy. Oxf Surv Evol Biol 7:45–67Google Scholar
  7. Baum DA (2009) Species as ranked taxa. Syst Biol 58:74–86Google Scholar
  8. Bickford D, Lohman DJ, Sodhi NS, Ng PK, Meier R, Winker K, Ingram KK, Das I (2007) Cryptic species as a window on diversity and conservation. Trends Ecol Evol 22:148–155Google Scholar
  9. Bock WJ (2004) Species: the concept, category and taxon. J Zool Syst Evol Res 42:178–190Google Scholar
  10. Bóna M (2011) A walk through combinatorics: an introduction to enumeration and graph theory. World Scientific, SingaporezbMATHGoogle Scholar
  11. De Queiroz K (2007) Species concepts and species delimitation. Syst Biol 56:879–886Google Scholar
  12. De Queiroz K, Donoghue MJ (1988) Phylogenetic systematics and the species problem. Cladistics 4:317–338Google Scholar
  13. Dress A, Moulton V, Steel M, Wu T (2010) Species, clusters and the ‘tree of life’: a graph-theoretic perspective. J Theor Biol 265:535–542MathSciNetGoogle Scholar
  14. Durrett R (2008) Probability models for DNA sequence evolution. Springer, New YorkzbMATHGoogle Scholar
  15. Etienne RS, Morlon H, Lambert A (2014) Estimating the duration of speciation from phylogenies. Evolution 68:2430–2440Google Scholar
  16. Fujisawa T, Barraclough TG (2013) Delimiting species using single-locus data and the generalized mixed yule coalescent (GMYC) approach: a revised method and evaluation on simulated datasets. Syst Biol 62:707–724Google Scholar
  17. Gascuel F, Ferrière R, Aguilée R, Lambert A (2015) How ecology and landscape dynamics shape phylogenetic trees. Syst Biol 64:590–607Google Scholar
  18. Graham CH, Fine PVA (2008) Phylogenetic beta diversity: linking ecological and evolutionary processes across space in time. Ecol Lett 11:1265–1277Google Scholar
  19. Hennig W (1965) Phylogenetic systematics. Annu Rev Entomol 10:97–116Google Scholar
  20. Hubbell SP (2001) The unified neutral theory of biodiversity and biogeography. Princeton University Press, PrincetonGoogle Scholar
  21. Hubbell SP (2003) Modes of speciation and the lifespans of species under neutrality: a response to the comment of Robert E. Ricklefs Oikos 100:193–199Google Scholar
  22. Hudson RR, Coyne JA (2002) Mathematical consequences of the genealogical species concept. Evolution 56:1557–1565Google Scholar
  23. Jabot F, Chave J (2009) Inferring the parameters of the neutral theory of biodiversity using phylogenetic information and implications for tropical forests. Ecol Lett 12:239–248Google Scholar
  24. Kopp M (2010) Speciation and the neutral theory of biodiversity. Bioessays 32:564–570Google Scholar
  25. Kwok RBH (2011) Phylogeny, genealogy and the linnaean hierarchy: a logical analysis. J Math Biol 63:73–108MathSciNetzbMATHGoogle Scholar
  26. Lambert A, Ma C (2015) The coalescent in peripatric metapopulations. J Appl Probab 52:538–557MathSciNetzbMATHGoogle Scholar
  27. Lambert A, Morlon H, Etienne RS (2015) The reconstructed tree in the lineage-based model of protracted speciation. J Math Biol 70:367–397MathSciNetzbMATHGoogle Scholar
  28. Maddison WP (1997) Gene trees in species trees. Syst Biol 46:523–536Google Scholar
  29. Manceau M, Lambert A, Morlon H (2015) Phylogenies support out-of-equilibrium models of biodiversity. Ecol Lett 18:347–356Google Scholar
  30. Mayden RL (1997) A hierarchy of species concepts: the denouement in the saga of the species problem. In: Claridge MF, Dawah HA, Wilson MR (eds) Species: the units of diversity. Chapman & Hall, pp 381–423Google Scholar
  31. Mehta RS, Bryant D, Rosenberg NA (2016) The probability of monophyly of a sample of gene lineages on a species tree. Proc Natl Acad Sci USA 113:8002–8009Google Scholar
  32. Melián CJ, Alonso D, Allesina S, Condit RS, Etienne RS (2012) Does sex speed up evolutionary rate and increase biodiversity? PLoS Comput Biol 8:1–9MathSciNetGoogle Scholar
  33. Missa O, Dytham C, Morlon H (2016) Understanding how biodiversity unfolds through time under neutral theory. Philos Trans R Soc B 371:20150226Google Scholar
  34. Morlon H (2014) Phylogenetic approaches for studying diversification. Ecol Lett 17:508–525Google Scholar
  35. Orr HA (1995) The population genetics of speciation: the evolution of hybrid incompatibilities. Genetics 139:1805–1813Google Scholar
  36. Pennell MW, Harmon LJ (2013) An integrative view of phylogenetic comparative methods: connections to population genetics, community ecology, and paleobiology. Ann NY Acad Sci 1289:90–105Google Scholar
  37. Puigbò P, Wolf YI, Koonin EV (2013) Seeing the tree of life behind the phylogenetic forest. BMC Biol 11:1–3Google Scholar
  38. Puillandre N, Lambert A, Brouillet S, Achaz G (2012) ABGD, automatic barcode gap discovery for primary species delimitation. Mol Ecol 21:1864–1877Google Scholar
  39. Pyron RA, Burbrink FT (2013) Phylogenetic estimates of speciation and extinction rates for testing ecological and evolutionary hypotheses. Trends Ecol Evol 28:729–736Google Scholar
  40. Regan CT (1925) Organic evolution. Nature 116:398–401Google Scholar
  41. Rosindell J, Cornell SJ, Hubbell SP, Etienne RS (2010) Protracted speciation revitalizes the neutral theory of biodiversity. Ecol Lett 13:716–727Google Scholar
  42. Rosindell J, Hubbell SP, Etienne RS (2011) The unified neutral theory of biodiversity and biogeography at age ten. Trends Ecol Evol 26:340–348Google Scholar
  43. Rosindell J, Harmon LJ, Etienne RS (2015) Unifying ecology and macroevolution with individual-based theory. Ecol Lett 18:472–482Google Scholar
  44. Samadi S, Barberousse A (2006) The tree, the network, and the species. Biol J Linn Soc 89:509–521Google Scholar
  45. Sneath PHA (1976) Phenetic taxonomy at the species level and above. Taxon 25:437–450Google Scholar
  46. Stadler T (2013) Recovering speciation and extinction dynamics based on phylogenies. J Evol Biol 26:1203–1219Google Scholar
  47. Steel M (2014) Tracing evolutionary links between species. Am Math Mon 121:771–792MathSciNetzbMATHGoogle Scholar
  48. Velasco JD (2008) Species concepts should not conflict with evolutionary history, but often do. Stud Hist Philos Biol. Biomed Sci 39:407–414Google Scholar
  49. Vences M, Guayasamin JM, Miralles A, De La Riva I (2013) To name or not to name: criteria to promote economy of change in linnaean classification schemes. Zootaxa 3636:201–244Google Scholar
  50. Yang Z, Rannala B (2010) Bayesian species delimitation using multilocus sequence data. Proc Natl Acad Sci USA 107:9264–9269Google Scholar

Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Center for Interdisciplinary Research in Biology (CIRB), Collège de FrancePSL Research University, CNRS UMR 7241, INSERM U1050ParisFrance
  2. 2.Institut de Biologie de l’École Normale Supérieure, École Normale SupérieurePSL Research University, CNRS UMR 8197, INSERM U1024ParisFrance
  3. 3.Laboratoire de Probabilités, Statistique et Modélisation (LPSM)Sorbonne Université, CNRS UMR 8001ParisFrance

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