Unaccounted Assumptions
Richard H. Zander
Res Botanical Web Site
Missouri Botanical Garden

December 22, 2005




unaccounted assumptions

R. H. Zander


There are many assumptions having to do with regularity and sample error significantly affecting the reliability of phylogenetic analysis, even purportedly Bayesian in nature, that are commonly ignored or incorrectly passed off as trivial in the speculative literature. The tree itself is a branching series of nested sets (e.g. the set of all taxa exhibiting certain state changes). A set may appear to be more definite a concept than a sample, yet it cannot be any better than the samples included in it, and a set is itself a sample.


As pointed out by Posada and Buckley (2004), statistical analysis commonly makes three fairly straight-forward but not easily checked assumptions:  that data sets are drawn from the same underlying process, that sample size is large enough to obtain meaningful results, and a multivariate normal distribution is involved.


Huelsenbeck and Rannala (2004), however, echo a common viewpoint in the literature downplaying the effect of many possible additional assumptions asserting that “the posterior probability of a tree is the probability that the tree is correct (assuming that the model is correct).” The likelihood principle, which states that the likelihood function contains all the information from the sample that is relevant for inferential and decision-making purposes (Winkler, 1972), is in this manner misused.


Some authors detail how their own study is robust to variation in certain major assumptions, but this is usually restricted to model selection and sequence alignment, while “robust” is never quantified probabilistically. Some recent papers (e.g. Engstrom et al., 2004) attempt to explore various dimensions of uncertainty aside from the analytic algorithm, but these papers are few, and the analysis is complex, and probabilities of less than 0.50 certainty generally are not precisely calculated and made to affect reliability measures given by other genes.


As few as six external factors that affect the reliability of internode branch arrangements each at 0.99 chance of being correct will reduce confidence in each branch arrangement to a maximum of 0.94 probability (as the product). Only if morphology agrees with the arrangement and is “uncontested” can it be used as a prior (here done at an arbitrarily assigned 0.95) that will ensure reliability of at least 0.95 via Bayes' Formula (if the reliability of the agreeing molecularly based branch arrangement is less than 0.95 and greater than 0.50).


Below is a list of presuppositions (variously discussed in general by, among others, Avise, 1994; Felsenstein, 2004; Huelsenbeck et al., 1994; Jenner, 2004; Kolaczkowski & Thornton, 2004; Lipscomb et al., 2003; Lyons-Weiler & Milinkovitch, 1997; Maddison, 1996; Naylor & Adams, 2003; Philippe et al., 1996; Pickett & Randle, 2005; Rokas et al., 2003; Ronquist, 2004; Ruedas et al., 2000; Sites et al., 1996; Templeton, 1986; Wendel & Doyle, 1998; Wilcox, et al., 2002). These can be important but are commonly not factored in, and this is especially true in the older literature. Some are obvious and major problems, and some are cryptic to the non-adept, or merely minor, or inapplicable to particular loci.


There are doubtless other factors, and each may affect the reliability of a branch arrangement of interest as the product of the confidence interval assigned the internode times the probability that each and every particular assumption is correct. It is doubtless possible to assign particular probabilities to at least some if not many of the assumptions below for particular data sets, but that task is beyond the scope of this paper. Commonly unaccounted (unfactored) assumptions or problems that could require reduction in branch arrangement reliability are included in the following several categories:


1. alternative alignments of DNA sequence data, including alignment by eye or computerized optimization for best fit; mistakes in assignment of homology of morphological characters (Hickson et al., 2000; Page, 2004; Wheeler, 1994, 1999);


2. avoiding using introns or especially emphasizing them for sometimes conflicting technical reasons (Pons et al., 2004; Engstrom et al., 2004);


3. BPP not lowered in a second study when reliability values in a previous study of less than 0.50 for the same lineages could be used as priors;


4. hybridization or reticulate evolution, unbalanced gene flow during introgression, gene conversion, chloroplast capture, paralogy or gene duplication (occasionally between organelles), conflation with orthology, recombination, heteroplasmy, haplotype polymorphism (Doyle et al., 2004; Holder et al., 2001; Jackson, 2005; Mason-Gamer, 2004; Popp & Oxelman, 2004; van Oppen et al., 2001; Wolfe & Randle, 2004);


5. clade probablilities not equal a priori (Pickett & Randle, 2005; Randle et al., 2005);


6. clocklike behavior or lack thereof, use of optimal model parameters in likelihood ratio test of molecular clock, use of nonparametric rate smoothing (Bromham & Woolfit, 2004; Sanderson, 1997);


7. concerted evolution (Nei et al., 2000; Popp & Oxelman, 2004);


8. convergence due to environmental selection on morphology or exons, assumed “neutral” mutations influenced by evolutionary pressures (Caporale, 2003; Doebley & Lukens, 1998; Rodriquez-Trelles et al., 2004; Zang & Kumar, 1997);


9. differences between consensus trees, best trees and true trees (Pagel et al., 2004);


10. differences between results of total evidence (combined data sets) and repeatability of results using separate gene and morphology evaluations, novel clades, using or not using different gene data at different levels in the tree; accepting data sets as compatible if non-corresponding clades lack a BP value >50% for each of two data set); random generation of traits shared by two sister lineages that is difficult to distinguish statistically from similar parallelism between each of the two sister lineages and the nearest neighbor lineage (Ané & Sanderson, 2005; Benton, 1999; Buckley et al., 2002; Chen et al., 2003; Eernisse & Kluge 1993; Engstrom et al., 2004; Johnson & Soltis, 1998; Nixon & Carpenter 1996; Nylander et al., 2004; Olmstead & Scotland, 2005; Scotland et al., 2003)


11. different results from different iterations, generations and replications of analysis processes, including Dollo or transversion parsimony, and ordered or unordered states, insufficient mixing and convergence of MCMC chains (Randle et al., 2005);


12. different results from parsimony, neighbor joining, maximum likelihood and Bayesian methods, or from the many different phylogenetic analytic software packages commonly used in the past 20 years, including ability to find shortest trees or proper trees in 0.95 credible interval, limited available selections of models or weighting (Douady et al., 2003; Felsenstein, 1978; Mindell & Thacker, 1996; Randle et al., 2005; Sober, 2004);


13. differential lineage sorting, i.e., different gene histories (Doyle, 1992, 1993; Hudson, 1992);


14. effect of uncertainty contributed by more or fewer taxa included in the data set, or the use of exemplar taxa to represent larger taxonomic units with presumably insignificant variation in traits among taxa, or the effect of inclusion or exclusion of problematic taxa, or selection of different or multiple outgroup(s); data per taxon sample size (Funk et al., 2004; Graybeal, 1998);


15. effect of under- and over-credibility of Bayesian analysis, Bayesian priors over-determining results with small data sets, extended lineages that are represented in a cladogram simply by an outer node may render the analysis imprecise because these sequences are unknown (Alfaro et al., 2003; Bininda-Emonds, 1996; Bollback, 2004; Churchill et al., 1992; Lewis et al., 2005);


16. genomic problems including differences between nucleotide- and amino acid-based analyses; codon bias in exons; reversal of asymmetric mutational constraints of strand nucleotide composition bias in mtDNA; possible strong selection pressure on strongly conserved non-coding sequences and persistent pseudogenes; limitations on congruence of orthologues; re-expression of pseudogenes; regulator- or promoter-switched deep homology masquerading as homoplasy (convergence); endogenous retroviruses causing portions of genome to appear to have a different evolutionary history (Bapteste et al., 2005; Barbulescu et al., 2001; Christianson, 2005; Collin & Cipriani, 2003; Hall, 2003; Hassanin et al., 2005; Hollyoake et al., 2005; Inagaki et al., 2004; Lockwood & Fleagle, 1999; Rohwer & Rudolph, 2005; Rokas et al., 2003).


17. heterogeneity of models among sites, heterogeneous evolutionary processes over phylogenetic history, nucleotide composition not constant over time (Goldman, 1993; Kolaczkowski & Thornton, 2004; Pagel & Meade, 2004; Tuffley & Steel, 1997);


18. inclusion or exclusion of fossil evidence (Smith & Turner, 2005);


19. incongruence, sometimes well supported, between mitrochondrial, chloroplast and nuclear data sets (Cronn et al., 2002; Des Marais & Mishler, 2002; Sang & Zhong, 2000; Shaw, 2002; Steppan et al., 2004; Wendel & Doyle, 1998);


20. inconsistent method leading to high bootstrap support for an incorrect clade (Cummings et al., 2003);


21. method of incorporation of indels and the effect on arrangements of interest, different gap costs (e.g., Pons et al., 2004; Simmons & Ochoterena, 2000);


22. model selection choice type and procedures, including amino acid and secondary structure, homogeneous versus heterogeneous models, choice between Bayesian or Akaike information criteria, too few data to ensure accuracy of likelihood ratio test, i.e. likelihood curve not shaped like a normal distribution, using 0.95 as significant for LRTs (Bollback, 2002; Buckley, 2002; Buckley et al., 2002; Pol, 2004; Posada & Buckley, 2004; Randle et al., 2005);


23. selecting and reusing data from taxa previously grouped by random rather high bootstrap or posterior probability; multiple test problems, e.g., one branch arrangement contrary to tradition among 20 arrangements each at 0.95 probability; (Felsenstein, 2004);


24. possibility of horizontal gene transfer (Davis & Wurdack, 2004; Nickrent et al., 2004);


25. rates other than gamma-distributed (Felsenstein, 2004; Pagel et al., 2004);


26. reliability values differing by method or only comparable between similarly sized clades (Picket & Randle, 2005; Sanjuán & Wróbel, 2005);


27. results affected by inclusion or exclusion of 3rd nucleotide position, high evolutionary rates making sequences unreliable, saturation, compositional heterogeneities, among-lineage and among-site heterogeneities, invariant sites, covariation, non-independence of characters, self-correction of flawed DNA; AFLP markers limited by unequal gain-loss probability, possible lack of independence, possible lack of homology (Engstrom et al., 2004; Ho & Jermiin, 2004; Koopman, 2005; Steppan et al., 2004; Sullivan & Swofford, 1997);


28. sample error, including misidentifications, uncertainty due to lack of vouchers, reagent contaminants, unreliable primers, laboratory mistakes, capture of data, software bugs, confirming DNA sequences by analysis of both forward and reverse strands or two different reactions from same individual; confirmation bias (the tendency to selectively notice and focus on evidence that supports a theory rather than on facts that might disprove it) (Bridge et al., 2003; Engstrom et al., 2004; Funk et al., 2005; Popp & Oxelman, 2004; Steppan et al., 2004; Vilgalys, 2003);


29. sample size of DNA sites;


30. serial extinctions of sister groups or strong anagenetic change modifying ancestral characters, variation in speed of molecular evolution or speciation versus variation in generation times;


31. uncertainty contributed by conflicting morphological results, statistical rejection of  morphological alternative topologies by the molecular and vice versa (Collard & Wood, 2000; Kirchoff et al., 2004; Steppan et al., 2004);


32. uncertainty introduced by choice of ACCTRAN and DELTRAN with PAUP* or rejection of both with MacClade (Donoghue & Ackerly, 1996; Maddison & Maddison, 1992; Swofford, 1998);


33. under- or overspecification or parameterization of the model, limitation of Metropolis coupling (Alfaro et al., 2003; Ericksson et al., 2003; Huelsenbeck & Rannala, 2004; Pagel et al., 2004);


34. unexpected stochastic effects, such as bad luck in exemplar choice, long-branch attraction, unusual noise (Hillis, 1991);


35. weighting inappropriately or variously, doubt in any rescaling or re-optimization, mistakes in use of statistics, use or non-use of “weeded” parsimony; trees not derived independently of the data sets used for testing (Engstrom et al., 2004; Goldman et al., 2000; Koopman, 2005; Milinkovitch et al., 1996; Engstrom et al., 2004).



Only a proportion of these assumptions affect any one study, yet even one problem can contribute significantly to uncertainty in any molecular analysis. For instance, a sequence alignment that is only 0.95 correct may affect a branch arrangement of interest if wrong. If that is the case, then the probability of the branch arrangement of interest being right (determined by likelihood/Bayesian analysis) must be multiplied by the probability that the sequence is correct; the branch arrangement has then 0.95 times 0.95 or 0.90 probability of being correct.


The user taxonomist should determine, to the extent possible, which assumptions are relevant, and how robust to each assumption are the published results, i.e. that there is either no change in branch arrangements of interest or, if so, whether the change is at a probability high enough to make the published arrangement unreliable. Commonly, insufficient data is provided in the original paper to even begin to do this adequately. One can use a general correction factor as a way around this problem, such as 0.01 penalty on each confidence or credible interval.



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[This is an extract with some modification of a larger paper just submitted.]