Rethinking phylogenetic comparative methods

In the paper

“The work of Beaulieu and O'Meara (Beaulieu et al. 2013;Beaulieu andO'Meara 2014, 2016) has illuminated important underlying reasons behind Rabosky and Goldberg's findings: the failure to consider alternative models in which the”

What the sources say

• ?Not checked — no full text of the sourcecites Beaulieu et al. 2013 source
• Supported

  In “Multimodel Inference and the Issue of Appropriate Models,” the paper explains that a complex diversification history can make a trait-dependent model fit even when the trait evolves independently of diversification. In “BiSSE HiSSE,” it says that including alternative trait-independent diversification models should alleviate spurious assignments of rate differences to observed traits. Page numbers are not available in the supplied copy. (LLM, conf=0.91)

  cites Beaulieu and O'Meara 2016 source

In the paper

“We think that the solution proposed by Beaulieu and O'Meara (2016)-accounting for background shifts in evolutionary regimes unrelated to the focal trait association-is general and applies across comparative biology.”

What the sources say

• Supported

  The paper describes expanding BiSSE to infer hidden states and including trait-independent diversification models alongside trait-dependent ones. In its BiSSE/HiSSE discussion, it says this should reduce spurious associations between diversification-rate differences and the focal trait. The claim that the approach applies across comparative biology is the citing authors’ own conclusion, not a result they attribute to this source. (LLM, conf=0.90)

  cites Beaulieu and O'Meara (2016) source

In the paper

“While this model is useful (and has often been used) for testing for adaptation, it is inconsistent with how we think of the process of adapting to an optimal state (Lande 1976;Hansen 1997;Hansen and Orzack 2005;Hansen et al. 2008;Hansen and Bartoszek 2012).”

What the sources say

• ?Not checked — no full text of the sourcecites Lande 1976 source
• Supported

  In “The Evolutionary Approach to a Primary Optimum” (page not available), Hansen describes adaptation as an approach toward an optimum. In “Results” (page not available), he says the model reduces to Brownian motion with a trend when the optimum is not reachable. This supports the cited contrast between Brownian motion and adaptation to an optimum. (LLM, conf=0.89)

  cites Hansen 1997 source

In the paper

“a wide breadth of macroevolutionary data suggest that abrupt shifts and discontinuities have been a major feature of life on Earth”

What the sources say

• Partly supported

  The paper’s opening section reports that a model combining rare, substantial bursts of phenotypic change with shorter-term bounded fluctuations best fits its data. But those data chiefly concern body size in mammals, squamates, and birds; they do not establish that abrupt shifts and discontinuities have been a major feature of life on Earth generally. (LLM, conf=0.85)

  cites Uyeda et al. 2011 sourceExperimental — accuracy not yet measured
• Partly supported

  The Abstract describes evidence of rapid evolutionary pulses in fossil and ecological data, and the Discussion reports that jump models best explained body-size evolution in 32% of the 66 vertebrate clades studied. These passages support abrupt shifts as a feature of evolution, but the claim extends the finding to life on Earth generally; the paper says the prevalence of pulsed evolution across the Tree of Life remains unknown. Page numbers were not available in our copy. (LLM, conf=0.86)

  cites Landis and Schraiber 2017 sourceExperimental — accuracy not yet measured
• Supported

  In “Scale and Hierarchy” (page unavailable), the paper describes fossil-record stasis and mass extinctions that redirect evolutionary trajectories rather than following trends observed over shorter intervals. In “Contingency” (page unavailable), it calls rare events part of the fabric of macroevolution. Together, these passages support the broad claim that discontinuities are a major macroevolutionary feature. (LLM, conf=0.86)

  cites Jablonski 2017 source

In the paper

“Hansen's introduction of the Ornstein-Uhlenbeck (OU) process to comparative biology and the suite of methods built on his approach have been the only real attempts to actually try and capture the basic dynamics of adaptive trait evolution on phylogenies.”

What the sources say

• Partly supported

  In “The Evolutionary Approach to a Primary Optimum” (page unavailable), Hansen identifies his model as an Ornstein–Uhlenbeck process and describes a novel biological interpretation of it. But he explicitly says the process had previously been suggested for comparative studies, so the paper does not support saying he introduced it to comparative biology. The Abstract describes his method, but does not establish that methods built on it were the only attempts to capture adaptive trait evolution on phylogenies. (LLM, conf=0.88)

  cites Hansen 1997 sourceExperimental — accuracy not yet measured

In the paper

“However, AIC provides only relative support for a model given a set of alternatives (see Pennell et al. 2015 for more on this point in the context of comparative methods).”

What the sources say

• Supported

  The Discussion (“Why Does Model Adequacy Matter?”) says that comparing a model with alternatives using information-theoretic metrics permits only a relative assessment of its suitability. The Results specifically use AIC to identify the most highly supported model in a candidate set. (LLM, conf=0.94)

  cites Pennell et al. 2015 source

In the paper

“Depending on the Bayesian network structure, the appropriate method of analysis can range from a nonphylogenetic regression (Fig. 7A), to commonly used comparative methods such as PGLS (Fig. 7B), to methods that require modeling both the evolutionary history of interaction of both trait X and trait Y (Fig. 7C) (Hansen 1997;Butler and King 2004;Hansen et al. 2008;Revell 2010;Hansen and Bartoszek 20”

What the sources say

• Partly supported

  The Phylogenetic Covariance section describes generalized least squares for phylogenetically correlated trait data, and the Discussion argues that comparative analyses should consider the history of selective regimes. The paper does not set out a Bayesian-network-based choice among nonphylogenetic regression, PGLS, and joint modeling of the evolutionary histories of two traits. Page numbers were not available in our copy. (LLM, conf=0.84)

  cites Hansen 1997 sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites Butler and King 2004 source
• ?Not checked — no full text of the sourcecites Hansen et al. 2008 source

In the paper

“For PGLS and other linear modeling approaches, modeling the errors using fat-tailed distributions (Blomberg et al. 2012;Landis et al. 2012;Elliot and Mooers 2014;Duchen et al. 2017) may mitigate the impact of singular evolutionary events on the estimation of the slope (also see Slater and Pennell 2013, for an alternative approach using robust regression).”

What the sources say

• ?Not checked — no full text of the sourcecites Blomberg et al. 2012 source
• Partly supported

  The paper’s introduction (page not available in our copy) says that Lévy-process jumps give trait-change distributions fat tails and account for abrupt evolutionary shifts. Its Discussion addresses detecting such jumps, but the paper does not show that fat-tailed errors mitigate their effect on slope estimates in PGLS or other linear models. (LLM, conf=0.82)

  cites Landis et al. 2012 sourceExperimental — accuracy not yet measured
• Partly supported

  The Background toy example shows that a heavy-tailed stable model is less affected than a Brownian model by an unusually large change on one branch, but its outcome is ancestral-state reconstruction, not a regression slope. The Discussion proposes heavy-tailed methods for future studies of correlated evolution and notes that stable distributions lack the covariance matrix used in phylogenetic regression. It does not show that fat-tailed errors mitigate the effect of singular events on slope estimates in PGLS or other linear models; page numbers were not provided in our copy. (LLM, conf=0.85)

  cites Elliot and Mooers 2014 sourceExperimental — accuracy not yet measured

In the paper

“The probability of the dependent model P(M dep |A) under Darwin's scenario is P(M dep |A) = (t/T) (7 )”

In the paper

“When we simulated data under the PE hypothesis, the estimated weight given to the PE hypothesis was likewise high (Fig. 3B).”

In the paper

“We can repeat the same exercise with more phylogenetically structured data (where the two clades of interest are fully bifurcating following a Yule process) and obtain identical results (Fig. 2, see Supplementary Material available on Dryad at http://dx.doi.org/10.5061/dryad.p8066hd).”

In the paper

“Therefore, the probability of the independent model denoted as P(M ind |A) given the assumptions above is P(M ind |A) = P(N x (t)|N x (T) ≥ 1)P(N y (t)|N y (T) ≥ 1) = (t/T) 2 , (6 )”

In the paper

“That single contrast results in a very highleverage statistical outlier that drives significance as the size of the shift increases (Fig. 2).”

In the paper

“Therefore, the test statistic D used in the likelihood ratio test for Pagel's discrete correlation test comparing models M ind and M dep is simply proportional to the ratio of the length of the branch where the shift occurred to the total length of the tree: D = 2(lnL(M dep )-lnL(M ind )) = 2(ln(t)-ln(T))-4(ln(t)-ln(T)) = 2(ln(T)-ln(t)).(8)”

In the paper

“even for the simple case of two continuous traits, we have shown how easily data simulated under the singular event model can result in highly significant regressions for OLS, PGLS, and IC regressions, regardless if the errors are simulated as independent or phylogenetically correlated with respect to the model and phylogeny.”

In the paper

“In this case, we recover high weights for the Phrynosomaonly hypothesis regardless if the model is fit to the Scales data set, or to data simulated under either the Phrynosoma-only hypothesis or the PE hypothesis.”

In the paper

“The likelihood value at the maximum likelihood estimate of this model turns out to be just the probability from Eq. ( 7), that is L(M dep ) = t/T.”

In the paper

“We find that our approach places intermediate weight on the PE hypothesis for the original Scales data set.”

In the paper

“Furthermore, the RJ portion of the model fit to the Scales data set recovers only a single highly supported shift on the stem branch of the Phrynosoma lizards (Fig. 3C,D).”

In the paper

“When data were simulated under the Phrynosoma-only hypothesis, the weight given to the PE hypothesis was low, as predicted (Fig. 3B).”

In the paper

“Looking at the reconstructions, it is also apparent that the PE hypothesis is the simplest model that allows a shift on the branch leading to Phrynosoma, a group that any herpetologist would identify as”

In the paper

“In no analysis did the reversible-jump portion recover support for any additional shifts.”

In the paper

“Plotting the empirically estimated differences in the MLEs against the predictions making the simplifying assumptions above reveals a strong modal correlation between them (Fig. 6).”

In the paper

“Notice that the empirical data set has intermediate weights.”

In the paper

“Points falling off the line represent slight violations of the assumptions we used to derive our prediction.”

In the paper

“Modest support for two additional shifts are recovered for the empirical data only (red circles).”

In the paper

“All analysis recover high weights.”

In the paper

“For example, we find that most comparative research questions have a poorly defined scope of inference: it is unclear to what population a model or inference should generalize to.”

In the paper

“These two causal structures are observationally equivalent-meaning that any distribution simulated under one can be replicated under the alternative causal structure.”

In the paper

“Their singular and unreplicated nature seems incompatible with models that we typically use to describe change over time, such as Brownian motion (BM; Felsenstein 1973) or the Mk model (Pagel 1994;Lewis 2001).”

What the sources say

• ?Not checked — no full text of the sourcecites Felsenstein 1973
• ?Not checked — no full text of the sourcecites Pagel 1994 source
• ?Not checked — no full text of the sourcecites Lewis 2001 source

In the paper

“We will show in each Case Study that rare evolutionary events may deceive our methods and distort our interpretations.”

In the paper

“Nevertheless, our primary point here is to suggest that the phenomenon that made Felsenstein's argument so intuitive is not the violation of i.i.d.errors but rather the biologically intuitive realization that unreplicated differences colocalized on a single branch provide only weak evidence of a causal relationship between traits.”

In the paper

“Maddison and FitzJohn (2015) recently demonstrated that common statistical tests (e.g., Maddison 1990;Pagel 1994) for the evolutionary correlation of discrete characters are prone to reporting a significant association even when the pattern is driven by a single (or, very few) independent transition(s) from one character state to another.”

What the sources say

• ?Not checked — no full text of the sourcecites Maddison and FitzJohn (2015) source

In the paper

“This seems to be a clear case of phylogenetic pseudoreplication (Read and Nee 1995;Maddison and FitzJohn 2015).”

What the sources say

• ?Not checked — no full text of the sourcecites Read and Nee 1995 source
• ?Not checked — no full text of the sourcecites Maddison and FitzJohn 2015 source

In the paper

“We will argue that this unresolved challenge permeates not just tests for discrete character correlations, but nearly every method of finding associations in comparative methods (Fig. 1).”

In the paper

“Guessing correctly which of the 42 branches on the phylogeny has a single shift with our hypothesis is rewarded by the analysis (we will return to this issue in Case Study III).”

In the paper

“In particular, the PE hypothesis fails to fully explain the shift leading to the Phrynosoma lizards (Fig. 3C,D), which are more extreme than they should be considering the other taxa in their regime (there is only one, Holbrookia maculata, which does not show such an extreme shift).”

In the paper

“Not only has this sowed widespread confusion in the literature about what PCMs are doing but has led us to develop methods that are susceptible to the very thing we sought to build defenses against-unreplicated evolutionary events.”

In the paper

“In their article, Maddison and FitzJohn (2015) simulated comparative data and reported a preponderance of significant results using Pagel's correlation test (1994) and Maddison's (1990) concentrated changes test.”

What the sources say

• ?Not checked — no full text of the sourcecites Maddison and FitzJohn (2015) source
• ?Not checked — no full text of the sourcecites Pagel (1994) source
• ?Not checked — no full text of the sourcecites Maddison (1990) source

In the paper

“Thus, our framework certainly does not automatically reward more complex, freely estimated models.”

In the paper

“In summary, the signal for an association between muscle fiber composition and predation escape behavior is generated in part, but not completely, by variation that is specific to the genus Phrynosoma.”

In the paper

“This suggests that the PE hypothesis has statistically supported explanatory power as its estimated weight is well bounded away from 0.”

In the paper

“Nevertheless, we show the value in combining a hypothesis-testing framework with a natural history approach to identifying patterns of evolution.”

In the paper

“As we mention above, Maddison and FitzJohn (2015) recently demonstrated that commonly used methods return significant correlations all the time—and in scenarios that seem to defy our statistical intuition.”

What the sources say

• ?Not checked — no full text of the sourcecites Maddison and FitzJohn (2015) source

In the paper

“But as recent controversies in phylogenetic comparative biology have highlighted, our current methods (reviewed in O'Meara 2012;Pennell and Harmon 2013;Garamszegi 2014) are not designed to deal with such dynamics.”

What the sources say

• ?Not checked — no full text of the sourcecites O'Meara 2012 source
• ?Not checked — no full text of the sourcecites Pennell and Harmon 2013 source
• ?Not checked — no full text of the sourcecites Garamszegi 2014 source

In the paper

“But the problems (and potential solutions) we identify apply just as well to situations where the background evolutionary dynamics change more frequently.”

In the paper

“After fitting the multioptimum OU models to the muscle fiber data, they find strong support for the PE hypothesis, which is 13.0 Akaike's Information Criterion (AICc) units better than the next closest model (FMPE).”

What the sources say

• ?Not checked — no full text of the sourcecites Scales et al. 2009 source

In the paper

“For these reasons, we argue that hypothesis-driven and phylogenetic natural history approaches are complementary: we must pit our particular causal hypotheses against a descriptive”

In the paper

“This is because accounting for the Phrynosoma shift is the primary feature of all three data sets (though weights are somewhat higher for data simulated under the Phrynosoma-only hypothesis than others).”

In the paper

“However, the analysis favors the Phrynosoma-only hypothesis simply because of the vague priors placed on the number and location of shifts in the reversible-jump analysis.”

In the paper

“The reasons for this are covered in Case Study I: these major shifts are likely to drown out any biological signal in a data set if they are unaccounted for by our hypothesisdriven models.”

In the paper

“For example, Pagel's (1994) correlation test would find the phylogenetic codistribution of milk production and middle ear bones highly statistically significant even though they both are a defining characteristic of mammals, an inference so obviously dubious that even Darwin (1872) warned against it.”

What the sources say

• ?Not checked — no full text of the sourcecites Pagel (1994) source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Darwin (1872)

In the paper

“Rather, standard linear regression assumes that the errors of the fitted model are independent and identically distributed (i.i.d.).”

In the paper

“This nonindependence can create apparent correlations between traits that, are in truth, evolving independently.”

In the paper

“Through three Case Studies, we demonstrate that the susceptibility to singular events is indeed a recurring problem in comparative biology that links several seemingly unrelated controversies.”

In the paper

“He then evolved traits according to a BM process along the phylogeny; he recovered a significant regression slope using Ordinary Least Squares (OLS) despite there being no evolutionary covariance between the traits.”

What the sources say

• ?Not checked — no full text of the sourcecites Felsenstein 1985 source

In the paper

“In statistical terms, this means that traits measured on one species will not be independent of traits measured on others.”

In the paper

“Nevertheless, the example illustrates that the phylogeny imposes a challenge to the inference of meaningful associations between traits not because it renders errors nonindependent, but because the structure of the phylogeny allows for ancient, potentially unknowable causal factors (which may be few or even singular) to drive widespread associations between traits.”

In the paper

“As stated above, the IC method is based on the BM model of trait evolution.”

What the sources say

• ?Not checked — no full text of the sourcecites Felsenstein 1985 source

In the paper

“if all of the phylogenetic signal in a data set is present in the predictor trait and the errors are i.i.d., then there is no need for any phylogenetic correction”

What the sources say

• ?Not checked — no full text of the sourcecites Rohlf 2001 source
• ?Not checked — no full text of the sourcecites Rohlf 2006 source

In the paper

“However, the intermediate result likely only occurs because the PE hypothesis places Phrynosoma in the same regime as Holbrookia maculata, which does not share the extreme shift that is found in Phrynosoma.”

In the paper

“By combining phylogenetic natural history approaches with our a priori hypotheses, we show that we can account for singular evolutionary events that are not well-accounted for by our generating model.”

In the paper

“However, as Pearl (2014) has convincingly demonstrated, Simpson's paradox is not really paradoxical at all when considered from the standpoint of Bayesian Networks.”

What the sources say

• ?Not checked — no full text of the sourcecites Pearl (2014) source

In the paper

“In contrast, if migratory behavior causes changes in body size, then selecting for an increase in body size will not result in a lineage changing their migratory status at all.”

In the paper

“Darwin's scenario-the singular origin of two coextensive traits on the phylogeny-represents a boundary case to finding the correlation between discrete characters.”

In the paper

“and remain poorly understood to this day (Hansen and Orzack 2005;Hansen and Bartoszek 2012).”

What the sources say

• ?Not checked — no full text of the sourcecites Hansen and Orzack 2005 source
• ?Not checked — no full text of the sourcecites Hansen and Bartoszek 2012 source

In the paper

“Rather, researchers' prior ideas about how traits map unto trees likely inform which traits they choose to test for correlated evolution.”

In the paper

“One clear case where such graphical modeling would improve inference are cases where considering phylogeny reverses the sign of the relationship between two variables.”

In the paper

“Under Darwin's scenario, including additional taxa in the analysis will increase the support for the dependent model simply as a consequence of increasing the total length of the tree (i.e., because T increases and the difference between ln(T) and ln(t) will get larger as long as the additional sampled taxa do not break Darwin's scenario).”

In the paper

“In other words, the results of the analysis are predetermined.”

In the paper

“As Maddison and FitzJohn (2015) point out, the traits we use in comparative analyses are not chosen independently with respect to their phylogenetic distribution (as we assumed in our analysis).”

What the sources say

• ?Not checked — no full text of the sourcecites Maddison and FitzJohn (2015) source

In the paper

“By working through the logic of comparative analyses using graphical models we have come to essentially the same line of reasoning of Westoby et al. (1995a,b), who, in the early days of PCMs, challenged the growing consensus that phylogeny needed to be included in any interspecific comparison-a consensus which has only gotten stronger as the years passed by (also see McNab 2003 for a related crit”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Westoby et al. (1995a,b)
• ?Not checked — no full text of the sourcecites McNab 2003 source

In the paper

“Pagel's correlation test for Darwin's scenario can essentially be reduced to the difference in probability between choosing the same branch twice vs. choosing the branch only once.”

In the paper

“Darwin's scenario-the singular origin of two coextensive traits on the phylogeny-represents a boundary case to finding the correlation between discrete characters.”

In the paper

“Here, increasing body size will only have a direct effect of decreasing species abundance, which is reflected in the estimate of the slope.”

In the paper

“We agree with Maddison and FitzJohn (2015) that this type of ascertainment bias is likely prevalent in empirical studies, even if it is usually more subtle than testing for a correlation between milk and middle ear bones.”

What the sources say

• ?Not checked — no full text of the sourcecites Maddison and FitzJohn (2015) source

In the paper

“This is precisely what Nee et al. (1991) found looking at the relationship between body size and abundance in British birds; depending on how they aggregated the data (means of species, means of genera, means of tribes, etc.) the direction of correlation flipped back and forth.”

What the sources say

• ?Not checked — no full text of the sourcecites Nee et al. (1991) source

In the paper

“In fact, Pearl shows that the appropriate way to analyze the data depends crucially on what one assumes is causing what.”

What the sources say

• ?Not checked — no full text of the sourcecites Pearl (2014) source

In the paper

“We have shown in the three Case Studies that many PCMs, including those that form the bedrock of our field, are susceptible to being misled by singular evolutionary events.”

In the paper

“For even a modestly sized tree, this coincidence is so unlikely that the alternative hypothesis of correlated evolution is preferred over the null.”

In the paper

“To estimate the net effect of B on N in network (A), the appropriate method of analysis is OLS regression (black line).”

In the paper

“Pagel's correlation test for Darwin's scenario can essentially be reduced to the difference in probability between choosing the same branch twice vs. choosing the branch only once.”

In the paper

“We emphasize that this implies that the use of phylogeny in interspecific comparisons is an assumption that depends on the precise question being asked and the hypothesized causal network.”

In the paper

“In cases where phylogeny does matter, we must specify the generating model for unobserved states in our causal graphs.”

In the paper

“It is therefore not completely unreasonable that Pagel's test tells us that these traits have evolved in an entirely correlated fashion.”

In the paper

“This asymmetry results in a what is known as a probabilistic Bayesian Network (a type of directed acyclic graph, or DAG) that predicts a specific set of conditional probabilities among the data.”

In the paper

“If only one event occurs however, this model is only distinguishable from graph (D) proportional to the probability that events K and L occur on the same branch (see Case Study III).”

In the paper

“Differences likely reflect the fact that we have not explicitly made the assumption that P(N x (t) = 1) = P(N y (t) = 1) ≈ 1 when we fit the model with diversitree.”

In the paper

“However, to estimate the effect of B in both networks, one must use different analytical approaches.”

In the paper

“However, BM and other continuous Gaussian or Markov processes are only a few of the many types of processes that may generate change on a phylogeny.”