Evolutionary Ecology

, Volume 33, Issue 6, pp 751–768 | Cite as

A multivariate phylogenetic comparative method incorporating a flexible function between discrete and continuous traits

  • Yuki HabaEmail author
  • Nobuyuki Kutsukake


One major challenge of using the phylogenetic comparative method (PCM) is the analysis of the evolution of interrelated continuous and discrete traits in a single multivariate statistical framework. In addition, more intricate parameters such as branch-specific directional selection have rarely been integrated into such multivariate PCM frameworks. Here, originally motivated to analyze the complex evolutionary trajectories of group size (continuous variable) and social systems (discrete variable) in African subterranean rodents, we develop a flexible approach using approximate Bayesian computation (ABC). Specifically, our multivariate ABC-PCM method allows the user to flexibly model an underlying latent evolutionary function between continuous and discrete traits. The ABC-PCM also simultaneously incorporates complex evolutionary parameters such as branch-specific selection. This study highlights the flexibility of ABC-PCMs in analyzing the evolution of phenotypic traits interrelated in a complex manner.


Phylogenetic comparative method (PCM) Approximate Bayesian computation (ABC) Multivariate analysis Social evolution African mole rats 



We would like to thank Dustin R. Rubenstein, Rafael Maia, and Margaret E. O’Brien at Columbia University and Jessica Zung at Princeton University for useful comments and advice. Masahito Tsuboi at University of Oslo also provided useful insights on the earlier version of manuscript. Two reviewers gave detailed and helpful comments on the manuscript. This study was financially supported by MEXT (No. 25711025) to K. N.

Author contributions

YH and KN conceived, designed, and performed the analysis. Both discussed the result and wrote the final manuscript.

Compliance with ethical standards

Conflict of interest

Both authors declare that they have no conflict of interest.

Supplementary material

10682_2019_10011_MOESM1_ESM.pdf (458 kb)
Supplementary material 1 (PDF 458 kb)
10682_2019_10011_MOESM2_ESM.docx (15 kb)
Supplementary material 2 (DOCX 15 kb)


  1. Beauchamp G (1999) The evolution of communal roosting in birds: origin and secondary losses. Behav Ecol 10:675–687Google Scholar
  2. Beaumont MA (2010) Approximate Bayesian computation in evolution and ecology. Ann Rev Ecol Evol Syst 41:379–406Google Scholar
  3. Beaumont MA, Zhang W, Balding DJ (2002) Approximate Bayesian computation in population genetics. Genetics 162:2025–2035PubMedPubMedCentralGoogle Scholar
  4. Bennett NC, Faulkes CG (2000) African mole-rats: ecology and eusociality. Cambridge University Press, CambridgeGoogle Scholar
  5. Bennett NC, Jarvis JUM, Cotterill FPD (1994) The colony structure and reproductive biology of the afrotropical Mashona mole-rat, Cryptomys darlingi. J Zool 234:477–487Google Scholar
  6. Bokma F (2010) Time, species, and separating their effects on trait variance in clades. Syst Biol 59:602–607PubMedGoogle Scholar
  7. Burda H, Kawalika M (1993) Evolution of eusociality in the Bathyergidae: the case of the giant mole-rat (Cryptomys mechowi). Naturwissenschaften 80:235–237PubMedGoogle Scholar
  8. Burda H, Honeycutt RL, Begall S, Locker-Grütjen O, Scharff A (2000) Are naked and common mole-rats eusocial and if so, why? Behav Ecol Sociobiol 47:293–303Google Scholar
  9. Csillery K, Blum MG, Gaggiotti OE, François O (2010) Approximate Bayesian computation (ABC) in practice. Trends Ecol Evol 25:410–418PubMedGoogle Scholar
  10. Duffy JM, Macdonald KS (2010) Kin structure, ecology and the evolution of social organization in shrimp: a comparative analysis. Proc R Soc B 277:575–584PubMedGoogle Scholar
  11. Emlen ST (1982) The evolution of helping. I. An ecological constraints model. Am Nat 119:29–39Google Scholar
  12. Faulkes CG, Bennett NC (2013) Plasticity and constraints on social evolution in African mole-rats: ultimate and proximate factors. Philos. T. R. Soc. B. 368:20120347Google Scholar
  13. Faulkes CG, Bennett NC, Bruford MW, O’brien HP, Aguilar GH, Jarvis JUM (1997) Ecological constraints drive social evolution in the African mole–rats. Proc R Soc B 264:1619–1627PubMedGoogle Scholar
  14. Faulkes CG, Verheyen E, Verheyen W, Jarvis JUM, Bennett NC (2004) Phylogeographical patterns of genetic divergence and speciation in African mole-rats (Family: Bathyergidae). Mol Ecol 13:613–629PubMedGoogle Scholar
  15. Felsenstein J (1985) Phylogenies and the comparative method. Am Nat 125:1–15Google Scholar
  16. Felsenstein J (2005) Using the quantitative genetic threshold model for inferences between and within species. Philos Trans R Soc B 360:1427–1434Google Scholar
  17. Felsenstein J (2012) A comparative method for both discrete and continuous characters using the threshold model. Am Nat 179:145–156PubMedGoogle Scholar
  18. Garamszegi LZ (2014) Modern phylogenetic comparative methods and their application in evolutionary biology: concepts and practice. Springer, HeidelbergGoogle Scholar
  19. Hadfield JD (2015) Increasing the efficiency of MCMC for hierarchical phylogenetic models of categorical traits using reduced mixed models. Methods Ecol Evol 6(6):706–714Google Scholar
  20. Hadfield JD, Nakagawa S (2009) General quantitative methods for comparative biology: phylogenies, taxonomies and multi-trait models for continuous and categorical characters. J Evol Biol 23:494–508Google Scholar
  21. Harano T, Kutsukake N (2018) Directional selection in the evolution of elongated upper canines in clouded leopards and sabre-toothed cats. J Evol Biol 31:1268–1283PubMedGoogle Scholar
  22. Harvey PH, Pagel MD (1991) The comparative method in evolutionary biology. Oxford University Press, OxfordGoogle Scholar
  23. Ives AR, Garland T (2010) Phylogenetic logistic regression for binary dependent variables. Syst Biol 59:9–26PubMedGoogle Scholar
  24. Ives AR, Garland T (2014) Phylogenetic regression for binary dependent variables. In: Garamszegi LZ (ed) Modern phylogenetic comparative methods and their application in evolutionary biology: concepts and practice. Springer, Heidelberg, pp 231–261Google Scholar
  25. Janzen T, Hoehna S, Etienne RS (2015) Approximate Bayesian computation of diversification rates from molecular phylogenies: introducing a new efficient summary statistic, the nLTT. Methods Ecol Evol 6:566–575Google Scholar
  26. Jarvis JUM (1981) Eusociality in a mammal: cooperative breeding in naked mole-rat colonies. Science 212:571–573PubMedGoogle Scholar
  27. Jarvis JUM, Bennett NC (1993) Eusociality has evolved independently in two genera of bathyergid mole-rats—but occurs in no other subterranean mammal. Behav Ecol Sociobiol 33:253–260Google Scholar
  28. Jones K, Bielby J, Cardillo M, Fritz S (2009) PanTHERIA: a species-level database of life history, ecology, and geography of extant and recently extinct mammals. Ecology 90:2648Google Scholar
  29. Kutsukake N, Innan H (2013) Simulation-based likelihood approach for evolutionary models of phenotypic traits on phylogeny. Evolution 67:355–367PubMedGoogle Scholar
  30. Kutsukake N, Innan H (2014) Detecting phenotypic selection by approximate Bayesian computation (ABC) in phylogenetic comparative methods. In: Garamszegi LZ (ed) Modern phylogenetic comparative methods and their application in evolutionary biology: concepts and practice. Springer, Heidelberg, pp 409–424Google Scholar
  31. Leuenberger C, Wegmann D (2010) Bayesian computation and model selection without likelihoods. Genetics 184:243–252PubMedPubMedCentralGoogle Scholar
  32. Lewis PO (2001) A likelihood approach to estimating phylogeny from discrete morphological character data. Syst Biol 50:913–925PubMedGoogle Scholar
  33. Marjoram P, Tavare S (2006) Modern computational approaches for analysing molecular genetic variation data. Nat Genet Rev 7:759–770Google Scholar
  34. Marjoram P, Molitor J, Plagnol V, Tavare S (2003) Markov chain Monte Carlo without likelihoods. Proc Natl Acad Sci USA 100:15324–15328PubMedGoogle Scholar
  35. Nunn CL (2011) The comparative approach in evolutionary anthropology and biology. University of Chicago Press, ChicagoGoogle Scholar
  36. Pagel M (1994) Detecting correlated evolution on phylogenies: a general method for the comparative analysis of discrete characters. Proc R Soc B 255:37–45Google Scholar
  37. R Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  38. Sheehan MJ, Botero CA, Hendry TA, Sedio BE, Jandt JM, Weiner S, Toth AL, Tibbetts EA (2015) Different axes of environmental variation explain the presence vs. extent of cooperative nest founding associations in Polistes paper wasps. Ecol Lett 18:1057–1067PubMedPubMedCentralGoogle Scholar
  39. Sherman PW, Jarvis JUM, Alexander RD (1991) The biology of the naked mole-rat. Princeton University Press, PrincetonGoogle Scholar
  40. Shultz S, Opie C, Atkinson QD (2011) Stepwise evolution of stable sociality in primates. Nature 479:219–222PubMedPubMedCentralGoogle Scholar
  41. Sichilima AM, Faulkes CG, Bennett NC (2008) Field evidence for a seasonality of reproduction and colony size in the Afrotropical giant mole-rat Fukomys mechowii (Rodentia: Bathyergidae). Afr Zool 43:144–149Google Scholar
  42. Sichilima AM, Bennett NC, Faulkes CG, Bronner GN (2011) Field evidence for colony size and aseasonality of breeding and in Ansell’s mole-rat, Fukomys anselli (Rodentia: Bathyergidae). Afr Zool 46:334–339Google Scholar
  43. Slater GJ, Harmon LJ, Wegmann D, Joyce P, Revell LJ, Alfaro ME (2012) Fitting models of continuous trait evolution to incompletely sampled comparative data using approximate Bayesian computation. Evolution 66:752–762PubMedGoogle Scholar
  44. Van Daele PA, Blonde P, Stjernstedt R, Adriaens D (2013) A new species of African mole-rat (Fukomys, Bathyergidae, Rodentia) from the Zaire-Zambezi watershed. Zootaxa 3636:171–189PubMedGoogle Scholar
  45. Wcislo WT, Danforth BN (1997) Secondarily solitary: the evolutionary loss of social behavior. Trends Ecol Evol 12:468–474PubMedGoogle Scholar
  46. Wright S (1934) An analysis of variablity in number of digits in an inbred strain of guniea pigs. Genetics 19(6):506–536PubMedPubMedCentralGoogle Scholar
  47. Young AJ, Jarvis JUM, Barnaville J, Bennett NC (2015) Workforce effects and the evolution of complex society in wild Damaraland mole rats. Am Nat 186:302–311PubMedGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Ecology and Evolutionary BiologyPrinceton UniversityPrincetonUSA
  2. 2.Department of Evolutionary Studies of Biosystems, SokendaiThe Graduate University for Advanced StudiesHayamaJapan

Personalised recommendations