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An Introduction to Phylogenetic Path Analysis

  • Alejandro Gonzalez-Voyer
  • Achaz von Hardenberg

Abstract

The questions addressed by macroevolutionary biologists are often impervious to experimental approaches, and alternative methods have to be adopted. The phylogenetic comparative approach is a very powerful one since it combines a large number of species and thus spans long periods of evolutionary change. However, there are limits to the inferences that can be drawn from the results, in part due to the limitations of the most commonly employed analytical methods. In this chapter, we show how confirmatory path analysis can be undertaken explicitly controlling for non-independence due to shared ancestry. The phylogenetic path analysis method we present allows researchers to move beyond the estimation of direct effects and analyze the relative importance of alternative causal models including direct and indirect paths of influence among variables. We begin the chapter with a general introduction to path analysis and then present a step-by-step guide to phylogenetic path analysis using the d-separation method. We also show how the known statistical problems associated with non-independence of data points due to shared ancestry become compounded in path analysis. We finish with a discussion about the potential effects of collinearity and measurement error, and a look toward possible future developments.

Notes

Acknowledgments

We thank László Zsolt Garamszegi for inviting us to write this chapter, as well as him and two anonymous referees for their useful comments and suggestions on a first draft of this chapter.

References

  1. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723CrossRefGoogle Scholar
  2. Arnold TW (2010) Uninformative parameters and model selection using Akaike’s information criterion. J Wildl Manage 74(6):1175–1178CrossRefGoogle Scholar
  3. Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach. Springer, New YorkGoogle Scholar
  4. Burnham KP, Anderson DR, Huyvaert KP (2011) AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons. Behav Ecol Sociobiol 65:23–35CrossRefGoogle Scholar
  5. Cardon M, Loot G, Grenouillet G, Blanchet S (2011) Host characteristics and environmental factors differentially drive the burden and pathogenicity of an ectoparasite: a multilevel causal analysis. J Anim Ecol 80:657–667CrossRefGoogle Scholar
  6. Felsenstein J (1985) Phylogenies and the comparative method. Am Nat 125(1):1–15CrossRefGoogle Scholar
  7. Fisher RA (1926) The design of experiments, 1st edn. Oliver and Boyd, EdinburghGoogle Scholar
  8. Freckleton RP (2009) The seven deadly sins of comparative analysis. J Evol Biol 22(7):1367–1375. doi: 10.1111/j.1420-9101.2009.01757.xCrossRefPubMedGoogle Scholar
  9. Freckleton RP (2011) Dealing with collinearity in behavioural and ecological data: model averaging and the problems of measurement error. Behav Ecol Sociobiol 65(1):91–101. doi: 10.1007/s00265-010-1045-6CrossRefGoogle Scholar
  10. Freckleton RP, Harvey PH, Pagel M (2002) Phylogenetic analysis and comparative data: a test and review of evidence. Am Nat 160(6):712–726. doi: 10.1086/343873CrossRefPubMedGoogle Scholar
  11. Garland TJ, Harvey PH, Ives AR (1992) Procedures for the analysis of comparative data using phylogenetically independent contrasts. Syst Biol 41:18–32CrossRefGoogle Scholar
  12. Geiger D, Verma T, Pearl J (1990) Identifying independence in Bayesian Networks. Networks 20:507–533CrossRefGoogle Scholar
  13. Grafen A (1989) The phylogenetic regression. Phil Trans Roy Soc B 326:119–157CrossRefGoogle Scholar
  14. Grewal R, Cote JA, Baumgartner H (2004) Multicollinearity and measurement error in structural equation models: Implications for theory testing. Mark Sci 23(4):519–529CrossRefGoogle Scholar
  15. Grim T (2008) A possible role of social activity to explain differences in publication output among ecologists. Oikos 117(4):484–487CrossRefGoogle Scholar
  16. Hansen TF (1997) Stabilizing selection and the comparative analysis of adaptation. Evolution 51(5):1341–1351CrossRefGoogle Scholar
  17. Harvey PH, Pagel MD (1991) The comparative method in evolutionary biology. Oxford University Press, OxfordGoogle Scholar
  18. Kline RB (2010) Principles and practice of structural equation modelling methodology in the social sciences, 3rd edn. Guilford Press, New YorkGoogle Scholar
  19. Lesku JA, Amlaner CJ, Lima SL (2006) A phylogenetic analysis of sleep architecture in mammals: the integration of anatomy, physiology, and ecology. Am Nat 168(4):441–443CrossRefGoogle Scholar
  20. Martins EP (2000) Adaptation and the comparative method. Trends Ecol Evol 15(7):296–299CrossRefGoogle Scholar
  21. Martins EP, Diniz-Filho JA, Housworth EA (2002) Adaptation and the comparative method: a computer simulation study. Evolution 56:1–13CrossRefGoogle Scholar
  22. Martins EP, Garland T (1991) Phylogenetic analyses of the correlated evolution of continuous characters: a simulation study. Evolution 45(3):534–557CrossRefGoogle Scholar
  23. Martins EP, Hansen TF (1997) Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into the analysis of interspecific data. Am Nat 149(4):646–667CrossRefGoogle Scholar
  24. Matthews R (2000) Storks deliver babies (p = 0.008). Teach Stat 22(2):36–38CrossRefGoogle Scholar
  25. Messerli FH (2012) Chocolate consumption, cognitive function, and Nobel laureates. New Engl J Med 367(16):1562–1564CrossRefGoogle Scholar
  26. Pagel M (1999) Inferring the historical patterns of biological evolution. Nature 401:877–884CrossRefGoogle Scholar
  27. Pagel M, Meade A (2006) Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov Chain Monte Carlo. Am Nat 167(6):808–825PubMedGoogle Scholar
  28. Pearl J (1988) Probabilistic reasoning in intelligent systems. Morgan and Kaufmann, San MateoGoogle Scholar
  29. Pearl J (2009) Causality: models, reasoning and inference. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  30. Petraitis PS, Dunham AE, Niewiarowski PH (1996) Inferring multiple causality: the limitations of path analysis. Funct Ecol 10:421–431CrossRefGoogle Scholar
  31. Pugesek BH, Grace JB (1998) On the utility of path modelling for ecological and evolutionary studies. Funct Ecol 12:853–856Google Scholar
  32. Pugesek BH, Tomer A (1995) Determination of selection gradients using multiple regression versus structural equation models (SEM). Biometrical J 37:449–462CrossRefGoogle Scholar
  33. Quader S, Isvaran K, Hale RE, Miner BG, Seavy NE (2004) Nonlinear relationships and phylogenetically independent contrasts. J Evol Biol 17:709–715. doi: 10.1111/j.1420-9101.2004.00697.xCrossRefPubMedGoogle Scholar
  34. Revell LJ (2010) Phylogenetic signal and linear regression on species data. Meth Ecol Evol 1(4):319–329. doi: 10.1111/j.2041-210X.2010.00044.xCrossRefGoogle Scholar
  35. Rohlf FJ (2006) A comment on phylogenetic correction. Evolution 60(7):1509–1515CrossRefGoogle Scholar
  36. Santos JC (2009) The implementation of phylogenetic structural equation modeling for biological data from variance-covariance matrices, phylogenies, and comparative analyses. The University of Texas at Austin, AustinGoogle Scholar
  37. Santos JC (2012) Fast molecular evolution associated with high active metabolic rates in poison frogs. Mol Biol Evol 29(8):2001–2018CrossRefGoogle Scholar
  38. Santos JC, Cannatella DC (2011) Phenotypic integration emerges from aposematism and scale in poison frogs. Proc Natl Acad Sci USAGoogle Scholar
  39. Shipley B (2000a) A new inferential test for path models based on directed acyclic graphs. Struct Equ Model 7(2):206–218CrossRefGoogle Scholar
  40. Shipley B (2000b) Cause and correlation in biology: a user’s guide to path analysis, structural equations and causal inference. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  41. Shipley B (2004) Analysing the allometry of multiple interacting traits. Perspect Plant Ecol Evol Syst 6(235):241Google Scholar
  42. Shipley B (2009) Confirmatory path analysis in a generalized multilevel context. Ecology 90:363–368CrossRefGoogle Scholar
  43. Shipley B (2013) The AIC model selection method applied to path analytic models compared using a d-separation test. Ecology 94(3):560–564CrossRefGoogle Scholar
  44. Stümpke H (1967) The Snouters: form and life of the Rhinogrades (trans: Doubleday & Company I). University of Chicago Press, ChicagoGoogle Scholar
  45. Team RDC (2013) R: A language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  46. Verma T, Pearl J (1988) Causal networks: semantics and expressiveness. In: Schachter R, Levitt TS, Kanal LN (eds) Uncertainty in artificial intelligence, vol 4. Elsevier, Amsterdam, pp 69–76Google Scholar
  47. von Hardenberg A, Gonzalez-Voyer A (2013) Disentangling evolutionary cause-effect relationships with phylogenetic confirmatory path analysis. Evolution 67(2):378–387. doi: 10.1111/j.1558-5646.2012.01790.xCrossRefGoogle Scholar
  48. Wilkinson GN, Rogers CE (1973) Symbolic description of factorial models for analysis of variance. Appl Stat 22(3):392–399CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alejandro Gonzalez-Voyer
    • 1
  • Achaz von Hardenberg
    • 2
  1. 1.Conservation and Evolutionary Genetics GroupEstación Biológica de Doñana (EBD-CSIC)SevillaSpain
  2. 2.Alpine Wildlife Research CentreGran Paradiso National ParkValsavarencheItaly

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