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Evolutionary analyses of intrinsically disordered regions reveal widespread signals of conservation [1]

['Marc D. Singleton', 'Howard Hughes Medical Institute', 'Uc Berkeley', 'Berkeley', 'California', 'United States Of America', 'Michael B. Eisen', 'Department Of Molecular', 'Cell Biology']

Date: 2024-05

Intrinsically disordered regions (IDRs) are segments of proteins without stable three-dimensional structures. As this flexibility allows them to interact with diverse binding partners, IDRs play key roles in cell signaling and gene expression. Despite the prevalence and importance of IDRs in eukaryotic proteomes and various biological processes, associating them with specific molecular functions remains a significant challenge due to their high rates of sequence evolution. However, by comparing the observed values of various IDR-associated properties against those generated under a simulated model of evolution, a recent study found most IDRs across the entire yeast proteome contain conserved features. Furthermore, it showed clusters of IDRs with common “evolutionary signatures,” i.e. patterns of conserved features, were associated with specific biological functions. To determine if similar patterns of conservation are found in the IDRs of other systems, in this work we applied a series of phylogenetic models to over 7,500 orthologous IDRs identified in the Drosophila genome to dissect the forces driving their evolution. By comparing models of constrained and unconstrained continuous trait evolution using the Brownian motion and Ornstein-Uhlenbeck models, respectively, we identified signals of widespread constraint, indicating conservation of distributed features is mechanism of IDR evolution common to multiple biological systems. In contrast to the previous study in yeast, however, we observed limited evidence of IDR clusters with specific biological functions, which suggests a more complex relationship between evolutionary constraints and function in the IDRs of multicellular organisms.

Proteins are the molecular machines that carry out many processes required for life at an atomic level. Though many proteins use fixed structures to perform their functions, proteins with flexible segments are widespread, especially in multicellular organisms. Furthermore, these intrinsically disordered regions (IDRs) are often involved in essential cellular functions. However, the sequences of IDRs evolve quickly, which challenges traditional bioinformatics methods that depend on sequence conservation to predict function. Several studies have demonstrated that distributed biophysical features of IDRs are constrained rather than their exact sequences, and a recent study in yeast found that IDRs with common patterns of conserved features were associated with specific functions. Therefore, in this work we ask if IDRs in fruit flies, another common laboratory organism, also have patterns of conservation with associated functions. We build on the previous study by integrating their approach into a fully statistical framework based on mathematical models of trait evolution. Though we identify widespread signals of conservation in the IDRs of fruit flies, we find less evidence of a simple relationship between features and function. These methods and results will provide a valuable resource that can guide future experimental analyses of IDRs in fruit flies and other organisms.

Data Availability: The code used to produce the results and analyses is available on GitHub at https://github.com/marcsingleton/IDR_evolution2023 . The following Python libraries were used: matplotlib [ 69 ], NumPy [ 70 ], pandas [ 71 ], SciPy [ 72 ], and scikit-learn [ 73 ]. Relevant output files, including the estimated parameters of the substitution, BM, and OU models, are available on Zenodo (DOI: 10.5281/zenodo.10308885 ). There are no primary data associated with this manuscript. All primary data are available from publicly accessible sources described in their corresponding sections.

Therefore, in this work we applied a series of phylogenetic models to dissect of evolution of a set of orthologous IDRs identified in the Drosophila genome. Our analyses span multiple levels, ranging from the sequences that compose these regions to the distributed features that characterize them as a whole. For the latter, though the previous approach relied on simulations to generate the null distribution for a hypothesis of no constraint, we instead leveraged a fully statistical phylogenetic comparative framework [ 32 ]. By comparing models of constrained and unconstrained continuous trait evolution, i.e. the Brownian motion and Ornstein-Uhlenbeck models, respectively, we can demonstrate evidence of selective constraint on features independent of any assumptions about the underlying process of sequence evolution. However, we also propose hybrid approaches that combine simulations with phylogenetic comparative methods to test increasingly refined models of IDR evolution. We found that IDRs exhibit unique patterns of amino acid substitution and that in some proteins disorder itself is a dynamically evolving property. Furthermore, though IDRs are broadly unconstrained along several axes of feature evolution, we identified signals of widespread constraint in IDRs, indicating conservation of distributed features is mechanism of IDR evolution common to multiple biological systems. Unlike in yeast, though, we observed limited evidence of IDR clusters with specific biological functions, which suggests a more complex relationship between evolutionary constraints and function in the IDRs of multicellular organisms. These conclusions, however, are tempered by several methodological limitations, e.g., the application of continuous models of trait evolution to discrete data, which are explored in greater detail in the discussion.

However, no known subsequent studies have determined if similar patterns of conservation are found in the IDRs of other systems. As another foundational model organism with abundant genomic information across many evolutionary lineages [ 24 – 27 ], the fruit fly, Drosophila melanogaster, is a natural choice for subsequent investigation. Furthermore, given its complex multicellular development process and shared signaling pathways with humans, the findings of such a study would significantly advance our understanding of the role of IDRs in gene regulation as well as human health and disease. The concordance of these results with the previously identified IDR clusters would also have profound implications for the broader mechanisms of IDR evolution. For example, the absence of global patterns of evolutionary signatures across IDRs in Drosophila would suggest they are property of IDRs which is unique to yeast. In contrast, the identification of clusters similar to those in yeast would support the existence of a taxonomy of IDRs which is conserved across the tree of life. The latter result would represent a significant step towards the creation of resources for the classification of IDRs analogous to those for folded domains such as Pfam [ 28 ], CATH [ 29 ], or SCOP [ 30 , 31 ].

The initial studies demonstrating evidence of constraint were generally restricted to specific features or proteins. However, by comparing the observed values of various IDR-associated properties against those generated under a simulated model of evolution, Zarin et al. [ 22 ] showed most IDRs across the entire yeast proteome contain conserved features. Furthermore, they identified clusters of IDRs with common “evolutionary signatures,” i.e. patterns of conserved features, which were associated with specific biological functions. This analysis for the first time provided a global view of the relationship between sequence and function in IDRs. A follow-up study then expanded on this initial finding by applying techniques from machine learning and statistics to predict the functions of individual IDRs using their evolutionary signatures [ 23 ].

This form of selective constraint can also describe the evolution of more “localized” features in IDRs such as short linear motifs (SLiMs). Because SLiMs are composed of fewer than 12 residues, they form limited interfaces that frequently mediate the transient binding events involved in signaling pathways [ 16 ]. Accordingly, they are highly enriched in IDRs, which provide an accessible and flexible scaffold for these interactions [ 17 , 18 ]. While some SLiMs in IDRs are strongly conserved at specific positions, these constitute a small fraction of disordered residues, estimated at roughly 17% in the yeast proteome [ 19 ]. Instead, as SLiMs are compact and often highly degenerate at some positions, they can arise de novo from a small number of mutations and therefore have high rates of turnover. Furthermore, when IDRs contain multiple copies of a motif that jointly mediate a high-avidity interaction [ 16 ] or a graded response to a signal via the accumulation of multiple phosphorylations [ 3 , 20 ], the individual motifs are under weak selective constraints. As a result, though SLiMs are encoded by specific sequences, in some contexts they may evolve as distributed features that characterize IDRs as a whole rather than specific sites within them [ 21 ].

Despite the prevalence and importance of IDRs in eukaryotic proteomes, associating them with specific molecular functions or biological processes remains a significant challenge. The sequences of IDRs are generally poorly conserved, so traditional bioinformatics approaches which rely on the conservation of amino acid sequences to identify homologous proteins and transfer annotations between them are largely unsuccessful when applied to IDRs. However, several recent studies have demonstrated evidence that IDRs are constrained to preserve “distributed features” such as flexibility [ 11 ], chemical composition [ 12 ], net charge [ 13 ], or charge distribution [ 14 , 15 ]. Because many sequences can yield a region with a specific composition, for example, this mode of constraint uncouples an IDR’s fitness from its strict sequence of amino acids. Furthermore, in contrast to folded regions whose precise contacts and packing geometries are easily disrupted by amino acid substitutions, distributed features are robust to such changes, as individual residues only weakly contribute to a region’s fitness. For example, a mutation at one site in an IDR that changes its net charge is easily reversed by subsequent compensatory mutations elsewhere in the region. Thus, under this model the sequences of IDRs can rapidly diverge and still preserve their structural or functional properties.

Intrinsically disordered regions (IDRs) are segments of proteins which lack stable three-dimensional structures and instead exist as ensembles of rapidly interconverting conformations [ 1 ]. As a result of this structural heterogeneity, IDRs can interact with diverse binding partners. Often these interactions have high specificity but moderate affinity, which permits the efficient propagation of signals by rapid binding and dissociation [ 2 , 3 ]. Furthermore, as IDRs readily expose their polypeptide chains, they are enriched in recognition motifs for post-translational modifications which allow environmental or physiological conditions to modulate their interactions. Accordingly, IDRs often act as the “hubs” of complex signaling networks by integrating signals from diverse pathways and coordinating interactions [ 4 , 5 ]. However, as IDRs are ubiquitous in eukaryotic proteomes, with estimates of the fractions of disordered residues in the human, mouse, and fruit fly proteomes ranging between 22 and 24% [ 6 , 7 ], they are involved in diverse processes [ 8 ] including transcriptional regulation [ 9 ] and the formation of biomolecular condensates [ 10 ].

Results

IDRs are shorter and more divergent than non-disordered regions As many IDRs evolve rapidly, a major challenge for proteome-wide comparative analyses is correctly inferring and aligning homologous IDRs. We therefore relied on a set of over 8,500 high quality alignments of full-length single copy orthologs from 33 species in the Drosophila genus which we had previously generated and characterized [33]. (The use of full-length single copy orthologs ensures that IDRs are properly aligned by “anchoring” them to more conserved regions and that the proteins are unlikely to have undergone functional divergence as a result of gene duplication.) We then identified regions with high levels of inferred intrinsic disorder using the disorder predictor AUCPreD [34]. To highlight the unique features of IDR evolution in subsequent analyses, we also extracted a complementary set of regions with low levels of inferred disorder. Both sets were filtered on several criteria, including the lengths of their sequences and their phylogenetic diversity, which yielded 11,445 and 14,927 regions, respectively, from 8,466 unique alignments. In the subsequent discussion, we refer to these sets as the “disorder” and “order” regions, respectively. To investigate the differences in basic sequence statistics between the two region sets, we first generated histograms from the average length of each region (S1 Fig). Although both distributions span several orders of magnitude, the order regions are generally longer than the disorder regions, with means of 245 and 105 residues, respectively. We then quantified the sequence divergence in each region by fitting phylogenetic trees to the alignments using amino acid and indel substitution models, which are probabilistic descriptions of sequence evolution that are parameterized in terms of the rates of change between residues or between aligned residues and gaps, respectively [35]. The average rates of substitution are significantly larger in the disorder regions, demonstrating that while both sets contain conserved and divergent regions, IDRs are enriched in more rapidly evolving sequences (S1 Fig). We also searched the database of Pfam domains against the full-length D. melanogaster proteins in these alignments and measured their overlap with the disorder and order regions. The results show the disorder set has a clear enrichment in regions with no or only small amounts of overlap relative to the order set, indicating that, compared to structured domains, IDRs are especially resistant to homology-based methods of functional annotation (S2 Fig).

IDRs have distinct patterns of residue substitution To gain insight into the substitution patterns of amino acid residues in the disorder and order regions, we fit substitution models to meta-alignments sampled from the respective regions. As these models are parameterized in terms of the one-way rates of change from one residue to another, the rates are not necessarily equal for a given pair when the initial and target residues are swapped. For example, the rate of change of valine to tryptophan can be distinct from that of tryptophan to valine. In practice, however, substitution models are typically constrained to fulfill a condition called time-reversibility, as this converts a difficult multivariate optimization of the tree’s branch lengths into a series of simpler univariate optimizations [36]. A common method for fulfilling this condition is parameterizing the model in terms of a frequency vector, π, and an exchangeability matrix, S. The frequency vector determines the model’s expected residue frequencies at equilibrium, meaning the model dictates that all sequences eventually approach this distribution, no matter their initial composition. The exchangeability matrix is symmetric (s ij = s ji ) and encodes the propensity for two residues to interconvert. Because the rate of change from residue i to residue j is given by r ij = s ij π j , higher exchangeability coefficients yield higher rates of conversion. Thus, exchangeability coefficients are frequently interpreted as a measure of biochemical similarity between residues. To highlight the differences in patterns of residue substitution between the disorder and order regions, the parameters in each model are directly compared in Fig 1, beginning with the frequency vectors. The disorder regions show an enrichment of “disorder-promoting” residues such as serine, proline, and alanine, and a depletion of hydrophobic and bulky residues such as trytophan and phenylalanine (Fig 1A). The exchangeability matrices fit to the disorder and order regions have similar overall patterns of high and low coefficients (Fig 1B–1C). However, the log ratios of the disorder to the order exchangeability coefficients show clear differences within and between the disorder-enriched and -depleted residues. The disorder-enriched residues are less exchangeable with each other, whereas disorder-depleted residues are more exchangeable with each other and with disorder-enriched residues (Fig 1D). Likewise, we observe a trend in the log ratios of the rate coefficients where the coefficients above the diagonal are generally positive, and those below the diagonal are generally negative (Fig 1E–1F). As the coefficients model the one-way rates of substitution between residues with the vertical and horizontal axes indicating the initial and target residues, respectively, this suggests a net flux towards a more disorder-like composition. Though, the coefficients between the disorder-depleted and -enriched classes of residues for both the exchangeability and rate matrices should be interpreted with caution, as they are estimated with a high amount of uncertainty (S6–S7 Figs). A second, more general, caveat is these trends may result from fitting substitution matrices to alignments which were created using other substitution matrices derived from alignments of largely structured proteins. However, as addressed in the discussion, their consistency with several similar analyses suggests they represent true differences in the substitution patterns of IDRs [37,38]. PPT PowerPoint slide

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TIFF original image Download: Fig 1. Amino acid substitution models fit to disorder and order regions. (A) Amino acid frequencies of substitution models. Amino acid symbols are ordered by their enrichment in disorder regions, calculated as the disorder-to-order ratio of their frequencies. Error bars represent standard deviations over models fit to different meta-alignments (n = 25). (B-C) Exchangeability coefficients of disorder and order regions, respectively, averaged over meta-alignments. (D) log 10 disorder-to-order ratios of exchangeability coefficients. (E-F) Rate coefficients of disorder and order regions, respectively, averaged over meta-alignments. The vertical and horizontal axes indicate the initial and target amino acids, respectively. (G) log 10 disorder-to-order ratios of rate coefficients. https://doi.org/10.1371/journal.pcbi.1012028.g001

Intrinsic disorder is poorly conserved in some proteins Though the substitution models reveal specific patterns of evolution at the level of individual residues, the large amounts of sequence divergence between many orthologous IDRs implies their evolution is not well-described by fine-scale models of residue substitution. Given the growing evidence that IDRs are constrained to conserve distributed properties, we instead turned towards characterizing their evolution in terms of 82 disorder-associated “molecular features” obtained from the previous study of IDRs in the yeast proteome. However, before conducting an in-depth analysis of these features, we examined the disorder score traces in greater detail and were struck by the significant variability between species. For each residue in the input sequence, AUCPreD returns a score between 0 and 1 where higher values indicate higher confidence in a prediction of intrinsic disorder. In some alignments, the disorder scores vary by nearly this entire range at a given position even when there is a relatively high level of sequence identity (Fig 2A). Though we cannot fully eliminate the possibility that this result is a prediction artifact, the strong performance of AUCPreD in a recent assessment of disorder predictors suggests the observed variability reflects true changes in these residues’ propensity for disorder [39]. PPT PowerPoint slide

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TIFF original image Download: Fig 2. Analyses of disorder scores. (A) Example region in the alignment of the sequences in orthologous group 07E3 with their corresponding disorder scores. Higher scores indicate a higher probability of intrinsic disorder. Disorder score traces are colored by the position of their associated species on the phylogenetic tree. (B) Correlations between disorder scores and feature contrasts in regions. Asterisks indicate statistically significant correlations as computed by permutation tests (p < 0.001). (C-D) Example scatter plots showing correlations given in panel B. (E) GO term analysis of regions with rapidly evolving disorder scores. Only terms where p < 0.001 are shown. https://doi.org/10.1371/journal.pcbi.1012028.g002 To better understand the relationship of this variability to differences in the regions’ biophysical properties, we sought to correlate the average disorder score of the segments in a region with their molecular features. However, as the sequences are not independent but instead related by a hierarchical structure which reflects their evolutionary relationships, any features derived from them are unsuitable for direct use in many standard statistical procedures. In the most severe cases, traits derived from clades of closely-related species can effectively act as duplicate observations, which can yield spurious correlations. We therefore applied the method of contrasts to both the disorder scores and the features [40,41]. This algorithm takes differences between adjacent nodes in the phylogenetic tree relating the species to generate “contrasts,” which, under some general assumptions of the underlying evolutionary process, are independent and identically-distributed and therefore appropriate for use in correlation analyses. (A sample calculation using this algorithm is shown in S8 Fig.) The resulting feature contrasts have varying degrees of correlation with the score contrasts (Fig 2B–2C). Some, like isopoint, are uncorrelated, but most are significantly, if weakly, correlated. In general, the strongest correlations are observed for features which have a direct biophysical relationship to the presence or absence of disorder, such as disorder_fraction or hydrophobicity. Interestingly, the correlations with many motifs were statistically significant, though small in magnitude relative to the non-motif features. However, a more detailed analysis of this observation is presented in the discussion. To determine if regions with rapidly evolving disorder scores are associated with particular functions, processes, or compartments, we then extracted the regions in the upper decile of the rate distribution and performed a term enrichment analysis on their associated annotations (S9 Fig). The most significant terms are generally related to DNA repair or extracellular structure, which suggests these processes and components are enriched in proteins whose structural state is rapidly evolving (Fig 2E).

IDRs have three axes of unconstrained variation Having calculated the features associated with the sequence segments composing each region in our data set, we then sought to determine if their distributions contained any global structure which would enable us to identify classes with distinct biophysical or functional properties. These distributions are generated by a complex underlying evolutionary process which reflects the combined effects of selection, drift, and mutation. However, to leverage a statistical framework to infer the properties of this process, we fit a Brownian motion (BM) model to each feature calculated from the segments in each region. BM is a simple model of evolution where continuous traits change through a series of small, undirected steps. Thus, the traits accumulate variation at a constant rate over time but do not on average deviate from their original values. BM models are therefore specified by two parameters: a rate ( ), which describes the speed at which trait variation accumulates, and a root (μ BM ), which describes the ancestral trait value. We then applied principal components analysis (PCA) to visualize the major axes of variation of the root and rate parameters for each feature and region. A difficulty with a direct analysis of the parameter estimates, however, is the sensitivity of PCA to differences in scaling between variables, and some features have dramatically different intrinsic scales. For example, many compositional features, like fraction_S, are restricted to the interval [0, 1], whereas SCD is unbounded and can vary from negative to positive infinity. As a result, SCD is responsible for a significant fraction of the overall variance in both parameter distributions (S10–S11 Figs). Therefore, we first normalized the parameters associated with each feature by transforming them into z-scores relative to their proteome-wide distributions. The first two principal components of the root distributions show little overall structure, though there is a slight enrichment of regions along two axes that correlate with acidic and polar features, respectively (S12 Fig). Likewise, the projections of the rates onto the first two principal components are largely distributed along the first (Fig 3A). This observation and the variable amounts of sequence divergence in the regions led us to suspect the first principal component was a measure of the overall rate of sequence evolution. Plotting the first principal component against the sum of the average amino acid and indel rates as measured by substitution models revealed a strong association (Fig 3B). We then projected the rates along second and third principal components to determine if these higher order components contained any additional structure. The resulting distribution is roughly triangular and contains three major axes of variation, corresponding to rapid changes in the regions’ proportions of glutamine, charged, and glycine residues (Fig 3C and 3D). Inspection of regions selected along these axes confirmed the high rates of evolution of these features (Fig 3E–3G). Furthermore, we observe a similar distribution when the rates of the order regions were projected along their second and third principal components, which suggests a lack of constraint along these axes is a general property of rapidly evolving proteins (S13 Fig). PPT PowerPoint slide

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TIFF original image Download: Fig 3. PCA of disorder regions’ feature rates. (A) The first two PCs of the disorder regions’ feature rate distributions. The explained variance percentage of each component is indicated in parentheses. (B) Scatter plot of the disorder regions’ feature rates along the first PC against the sum of the average amino acid and indel substitution rates in those regions. (C) The second and third PCs of the disorder regions’ feature rate distributions. The explained variance percentage of each component is indicated in parentheses in the axis labels. (D) The same plot as panel C with the projections of original variables onto the components shown as arrows. Only the 16 features with the largest projections are shown. Scaling of the arrows is arbitrary. (E-G) Example alignments of disorder regions from the orthologous groups 0A8A, 3139, 04B0, respectively. The colored bars on the left indicate the hexbin containing that region in panel C. https://doi.org/10.1371/journal.pcbi.1012028.g003

A model of constrained evolution can identify signals of conservation Though the BM process permits the inference of the rates of feature evolution after accounting for the phylogenetic relationships between species, it does not directly test for their conservation. In fact, under the BM model, trait variation is unconstrained and will increase without bound over time. Instead, evidence of conservation requires comparison to a model where trait variation is constrained. A common choice for modeling the effect of selection on the evolution of a continuous trait is the Ornstein-Uhlenbeck (OU) model. The OU model is similar to the BM model where a trait accumulates variation through a series of small, undirected steps. However, it differs in that the trait is also attracted towards an optimal value where the attraction is proportional to the trait’s distance from this value. Under an additional assumption of stationarity that ensures parameter identifiability and estimate consistency, the OU model is accordingly specified with three total parameters: the optimal value (μ OU ), the fluctuation magnitude ( ), and the selection strength (α) [42,43]. While the first two parameters are analogous to the root and rate parameters in the BM model, respectively, the selection strength has no equivalent. As both models are fully probabilistic, the data’s support for the OU model relative to the BM model is quantified by the log ratio of their likelihoods, with greater values indicating more support for the OU model. However, to empirically relate these values to type I and II error rates under a hypothesis testing framework and to assess other statistical properties of the models, we simulated data under each model with a range of values for each of its parameters. Because the likelihood of both models is unchanged if the mean and observations are shifted by a constant, we fixed the mean and optimal values of the BM and OU models to zero in our simulations. The results show the rate of the BM model is accurately estimated over several orders of magnitude (Fig 4A). Additionally, the variance of these estimates is proportional to the magnitude of the rate, indicated by the constant height of the violin plots in log scale. In contrast, the estimate of the rate of the OU model can have significant bias depending on relative values of the true parameters. For example, in the lower left, when is accurately estimated, as α is small relative to (Fig 4B). In the central band, however, when is overestimated, as some movement towards the optimal value is likely attributed to a greater fluctuation magnitude. Finally, in the upper right, when is underestimated, as movement from the restoring force overwhelms the contribution of the stochastic component. Similarly, the estimate of the selection strength is biased for many parameter value combinations, though the relationship is more complex (Fig 4C). PPT PowerPoint slide

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TIFF original image Download: Fig 4. Hypothesis testing statistics under simulated BM and OU models. (A) Violin plots of the estimated rates as a function of the true rates ( ) under the BM model. (B) log 10 ratio of the mean estimated rate over its true value as a function of the true rates ( ) and selection strengths (α). (C) log 10 ratio of the mean estimated selection strength over its true value as a function of the true rates ( ) and selection strengths (α). (D) The probability of incorrectly rejecting the BM model in favor of the OU model (type I error) as a function of a given critical value of the log likelihood ratio. Each line indicates a different value of the true rate under the BM model. (E) Type I error as a function of a given critical value as in panel D but with all simulations under different values of the true rate combined into a single data set. (F) The probability of incorrectly failing to reject the BM model in favor of the OU model (type II error) as a function of the true rates ( ) and selection strengths (α). The probabilities were calculated using the critical value obtained from the empirical 1% type I error rate shown in panel E. https://doi.org/10.1371/journal.pcbi.1012028.g004 We then quantified the type I and II error rates under a hypothesis testing framework. We first calculated the type I error rate as a function of the critical value of the log likelihood ratio for each value of the BM rate separately (Fig 4D). As the overlapping curves indicate the ratios are independent of the true value, we merged the simulations and calculated empirical critical values for 5% (2.58) and 1% (4.20) type I error rates (Fig 4E). Using the 1% critical value, we calculated the type II error rate as a function of the OU parameter values (Fig 4F). The results show a strong dependence on the log ratio of α to , with the error rate sharply declining to zero when . In summary, these results demonstrate that while the parameter estimates of the OU model can have significant bias, when selection is strong relative to the fluctuation magnitude, the log likelihood ratio of the two models can reliably signal against a null hypothesis of Brownian motion.

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