8.4 Evolutionary Models and Tree Evaluation
5 min read•july 30, 2024
Evolutionary models are the backbone of phylogenetic analysis. They describe how DNA and protein sequences change over time, helping us figure out how species are related. These models are crucial for building accurate family trees of life.
Tree evaluation methods like and Bayesian tell us how reliable our phylogenetic trees are. By understanding model selection and tree support, we can better interpret evolutionary relationships and make sense of life's history.
Evolutionary Models in Phylogenetics
Mathematical Descriptions of Sequence Change
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- Evolutionary models mathematically describe DNA or protein sequence changes over time
- Account for factors influencing molecular evolution (nucleotide substitution rates, transition/transversion biases, site-specific rate variation)
- Calculate likelihood of observed sequence data given tree topology and branch lengths
- Crucial for accurate estimation of phylogenetic relationships and divergence times
- Incorporated into methods like maximum likelihood and for tree reconstruction
- Correct for multiple substitutions at the same site preventing underestimation of evolutionary distances
Applications in Phylogenetic Analysis
- Essential for accurate phylogenetic inference
- Used in maximum likelihood and Bayesian methods to reconstruct phylogenetic trees
- Help choose appropriate models for specific research questions
- Provide insights into evolutionary processes acting on sequences
- Allow comparison of different evolutionary hypotheses
- Enable estimation of ancestral sequences and character states
Substitution Models for Sequence Evolution
Basic Nucleotide Substitution Models
- Jukes-Cantor (JC69) model assumes equal base frequencies and substitution rates between all nucleotides
- Kimura two-parameter (K2P) model extends JC69 by distinguishing between transition and transversion rates
- Allows for transition bias commonly observed in DNA sequences
- More complex models like HKY85 and GTR incorporate additional parameters
- Account for unequal base frequencies
- Allow variable substitution rates between different nucleotide pairs
- Selection of appropriate model depends on sequence data type and required complexity level
Protein Substitution Models
- PAM () matrices model amino acid substitutions over evolutionary time
- Based on observed changes in closely related proteins
- BLOSUM () matrices derived from local alignments of more distantly related proteins
- Incorporate physiochemical properties of amino acids in substitution probabilities
- Different matrices optimized for various evolutionary distances (PAM1, PAM250, BLOSUM62)
Model Application and Parameter Estimation
- Calculate for different time intervals
- Estimate model parameters from observed sequence data
- Maximum likelihood or Bayesian methods often used for parameter estimation
- Consider trade-offs between model complexity and computational requirements
- Understand assumptions and limitations of each model for proper interpretation
- Examples of parameter estimation:
- Estimating transition/transversion ratio in K2P model
- Inferring base frequencies in more complex models like GTR
Model Fit for Sequence Data
Model Selection Techniques
- (LRT) compares nested models
- Determines if additional parameters significantly improve fit
- Calculates difference in log-likelihood between models
- Compares to chi-square distribution to assess significance
- (AIC) balances model fit against complexity
- AIC = 2k - 2ln(L), where k number of parameters, L maximized likelihood value
- Lower AIC indicates better model
- (BIC) similar to AIC but penalizes complexity more strongly
- BIC = ln(n)k - 2ln(L), where n sample size, k number of parameters, L maximized likelihood value
- Cross-validation assesses model performance on independent data sets
- Helps prevent overfitting by testing model on data not used in parameter estimation
Automated Model Selection Tools
- and automate process of comparing multiple models
- Implement various model selection criteria (LRT, AIC, BIC)
- Provide statistical comparisons and rankings of different models
- Generate model parameter estimates for selected best-fit model
- Visualize relative fit of different models to aid in selection process
Biological Implications of Model Selection
- Best-fitting model provides insights into evolutionary processes acting on sequences
- May reveal patterns of nucleotide or amino acid substitution bias
- Can indicate presence of rate heterogeneity across sites
- Helps identify appropriate level of model complexity for dataset
- Informs choice of models for subsequent analyses (phylogenetic reconstruction, divergence time estimation)
Phylogenetic Tree Support
Bootstrap Analysis
- Resampling technique estimates reliability of branches in phylogenetic trees
- Process creates multiple datasets by resampling original data with replacement
- Reconstructs trees for each resampled dataset
- Bootstrap support values represent percentage of resampled trees containing particular clade
- Indicates robustness of groupings in
- Generally, values >70% considered moderate support, >90% strong support
- Example: 1000 bootstrap replicates performed, clade appears in 850 resulting trees, bootstrap support 85%
Bayesian Posterior Probabilities
- Represent probability of clade being true given data and model in Bayesian analysis
- Calculated using Markov chain Monte Carlo (MCMC) methods
- Sample trees from posterior distribution of possible trees
- Posterior probability of clade calculated as proportion of sampled trees containing that clade
- Often yield higher support values compared to bootstrap analysis
- Example: Clade appears in 950 out of 1000 trees sampled from posterior distribution, posterior probability 0.95
Interpreting Support Values
- Bootstrap values and posterior probabilities not directly comparable
- Consider factors affecting support:
- Taxon sampling (number and diversity of included species)
- Sequence length and informativeness
- Model adequacy and fit to data
- Low support may indicate:
- Rapid diversification events
- Conflicting phylogenetic signal
- Insufficient data to resolve relationships
- High support does not guarantee accuracy, may result from systematic biases
- Combine multiple support measures for comprehensive assessment of tree reliability
Interpreting Phylogenetic Studies
Evaluating Methodological Choices
- Assess appropriateness of chosen evolutionary model for data and research question
- Evaluate tree reconstruction method (maximum likelihood, Bayesian inference, parsimony)
- Examine quality and comprehensiveness of sequence data:
- Taxon sampling strategy
- Alignment methods used
- Treatment of missing data or gaps
- Consider potential sources of systematic error:
- Long-branch attraction
- Incomplete lineage sorting
- Horizontal gene transfer
Analyzing Results and Support
- Examine reported measures of tree support (bootstrap values, posterior probabilities)
- Interpret support values in context of study and data limitations
- Assess congruence between phylogenetic results and other evidence:
- Morphological data
- Biogeographical patterns
- Fossil record
- Evaluate biological implications of inferred phylogeny:
- Evolutionary relationships between taxa
- Timing of diversification events
- Patterns of character evolution
Critical Assessment of Study
- Analyze authors' discussion of limitations and alternative interpretations
- Evaluate suggestions for future research to improve phylogenetic inference
- Consider potential biases in taxon sampling or gene selection
- Assess impact of missing data or unresolved relationships on conclusions
- Examine how well phylogenetic results address initial research questions
- Identify areas where additional data or analyses could strengthen conclusions
Key Terms to Review (26)
Akaike Information Criterion: The Akaike Information Criterion (AIC) is a statistical tool used for model selection, which evaluates how well a model explains the data while penalizing for the complexity of the model. AIC provides a relative measure of the information lost when a particular model is used, helping researchers choose between competing models by balancing goodness-of-fit and model simplicity. It is particularly useful in evolutionary biology for comparing different models of evolutionary processes and in molecular biology for assessing statistical distributions of biological data.
Bayesian Inference: Bayesian inference is a statistical method that applies Bayes' theorem to update the probability of a hypothesis as more evidence or information becomes available. This approach allows researchers to incorporate prior knowledge alongside new data, making it particularly useful in fields like bioinformatics and molecular biology for interpreting complex biological data.
Bayesian Information Criterion: The Bayesian Information Criterion (BIC) is a statistical tool used to evaluate and compare different models, especially in the context of likelihood estimation. It helps in model selection by balancing the goodness of fit against the complexity of the model. BIC is particularly useful in situations where a trade-off between model accuracy and overfitting is necessary, making it relevant in both evolutionary modeling and statistical distributions in molecular biology.
Beast: In the context of molecular evolution, a 'beast' refers to a computational framework used for estimating phylogenies, divergence times, and other evolutionary parameters using molecular data. This term is closely tied to Bayesian methods and provides a flexible platform for modeling complex evolutionary processes by combining molecular sequences with known biological information, allowing researchers to make inferences about evolutionary relationships and timelines.
Blocks substitution matrix: A blocks substitution matrix is a type of scoring matrix used in molecular biology to evaluate the similarity of sequences by quantifying the probability of substitutions between different amino acids or nucleotides. These matrices provide a structured approach for aligning sequences based on evolutionary relationships, allowing researchers to model how sequences evolve over time and assess the significance of alignments in phylogenetic analyses.
Bootstrap analysis: Bootstrap analysis is a statistical method used to estimate the accuracy of a sample statistic by resampling with replacement from the original data set. This technique is particularly valuable in molecular biology, as it helps in assessing the confidence levels of phylogenetic trees and aligning sequences, providing insight into the reliability of the inferred relationships and structures.
Cladogram: A cladogram is a diagram that illustrates the evolutionary relationships among various biological species or entities, based on shared characteristics and common ancestry. This branching tree-like structure helps in visualizing how species diverged from one another over time and is used to represent hypotheses about the evolutionary history of these organisms.
Confidence Intervals: A confidence interval is a statistical tool that provides a range of values, derived from sample data, that is likely to contain the true population parameter with a specified level of confidence. This concept is crucial for making inferences about evolutionary models and assessing the uncertainty of estimates in tree evaluation, as it helps researchers quantify the degree of certainty in their findings.
Homology: Homology refers to the similarity in sequence or structure between biological molecules, such as proteins or nucleic acids, due to shared ancestry. This concept is essential in comparing sequences and constructing phylogenetic relationships, as it allows researchers to identify conserved regions that may have important functional roles.
Jackknife resampling: Jackknife resampling is a statistical technique used to estimate the variability of a sample statistic by systematically leaving out one observation at a time and recalculating the statistic based on the remaining data. This method helps in assessing the stability and reliability of estimates, making it useful for various analyses, particularly in cases where data sets are small or have potential biases. It can be applied in evaluating multiple sequence alignments, estimating parameters in evolutionary models, and assessing clustering algorithms by providing insights into their robustness.
Jmodeltest: jmodeltest is a software tool used for model selection and evaluation in phylogenetics, particularly for selecting the best-fitting evolutionary models for DNA or protein sequences. This program assists researchers in analyzing molecular data by providing a range of statistical tests to compare models, which is crucial for constructing accurate phylogenetic trees and understanding evolutionary relationships.
Likelihood Ratio Test: The likelihood ratio test is a statistical method used to compare the goodness of fit of two competing models, often a null hypothesis model and an alternative hypothesis model. This test evaluates whether the observed data is more likely under one model versus the other by calculating the ratio of their likelihoods. It's particularly important in molecular biology for assessing models of nucleotide and amino acid substitutions, as well as in evaluating evolutionary trees.
Maximum Likelihood Estimation: Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probabilistic model, aiming to find the parameter values that maximize the likelihood of observing the given data. This method is crucial in various applications within molecular biology, especially in modeling sequences and phylogenetics, as it helps infer parameters that best explain the observed biological data.
Modeltest: Modeltest is a statistical procedure used to evaluate different evolutionary models to determine which one best fits a given set of genetic data. This process is crucial in phylogenetics, where selecting the appropriate model can significantly affect the inference of evolutionary relationships and the accuracy of tree estimations.
Molecular clock: A molecular clock is a technique used to estimate the time of evolutionary events based on the rate of molecular change in DNA or protein sequences. This method assumes that mutations accumulate at a relatively constant rate over time, allowing scientists to infer the timing of divergences among species. The molecular clock is essential in understanding evolutionary relationships and in constructing phylogenetic trees.
Monophyletic group: A monophyletic group, or clade, consists of an ancestor and all of its descendants, representing a complete branch of the evolutionary tree. This grouping is essential for understanding evolutionary relationships as it highlights common ancestry and helps in constructing accurate phylogenetic trees. Recognizing monophyletic groups ensures that classifications reflect true evolutionary lineage rather than arbitrary similarities.
Neighbor-joining algorithm: The neighbor-joining algorithm is a distance-based method used to construct phylogenetic trees, which visually represent the evolutionary relationships between species. This algorithm efficiently calculates a tree by identifying pairs of taxa that minimize the total branch length, allowing for quick and accurate tree construction. It is particularly useful for large datasets and can incorporate various evolutionary models to enhance its accuracy.
Orthologs: Orthologs are genes in different species that evolved from a common ancestral gene through speciation and retain the same function. They provide insights into evolutionary relationships and are crucial for understanding gene functions across different organisms, making them important in various fields such as comparative genomics, evolutionary biology, and functional annotation.
Paraphyletic group: A paraphyletic group is a type of biological classification that includes a common ancestor and some, but not all, of its descendants. This classification can lead to a misunderstanding of evolutionary relationships because it does not encompass all the descendants of the ancestor, creating gaps in the tree of life. Paraphyletic groups are often contrasted with monophyletic groups, which include an ancestor and all its descendants, and polyphyletic groups, which do not include the common ancestor at all.
Phylogenetic tree: A phylogenetic tree is a graphical representation that illustrates the evolutionary relationships among various biological species or entities based on similarities and differences in their physical or genetic characteristics. It showcases how species have diverged from common ancestors over time, and helps in understanding the history of evolution. These trees are crucial in studying molecular evolution, as they can be constructed using multiple sequence alignment data, and serve as a foundation for both distance-based and character-based phylogenetic methods.
Point Accepted Mutation: A point accepted mutation is a specific type of genetic change where a single nucleotide in the DNA sequence is replaced with another nucleotide, and this change is tolerated by the organism, resulting in a phenotype that does not significantly differ from the original. These mutations play a crucial role in evolutionary processes, as they can lead to variations that are neutral or beneficial, influencing genetic diversity and adaptation over time.
Posterior Probabilities: Posterior probabilities represent the updated probabilities of a hypothesis after considering new evidence. This concept is central to Bayesian statistics, where prior beliefs are combined with observed data to refine estimates about parameters or states, helping in decision-making processes in various fields, including bioinformatics and evolutionary biology.
Raxml: RAxML (Randomized Axelerated Maximum Likelihood) is a software program used for constructing phylogenetic trees based on maximum likelihood estimation. It is particularly useful for analyzing large datasets and has become a standard tool in computational biology for inferring evolutionary relationships among species or genes, leveraging different models of sequence evolution.
Substitution models: Substitution models are mathematical frameworks used to describe the processes of nucleotide or amino acid changes in sequences over time. They provide a way to estimate how these changes occur in evolutionary biology, aiding in the construction and evaluation of phylogenetic trees by determining the likelihood of observed sequence data under different evolutionary scenarios.
Transition Probability Matrices: Transition probability matrices are mathematical constructs used to describe the probabilities of transitioning from one state to another within a stochastic process. These matrices are especially important in evolutionary models, where they help to quantify how likely it is for a species to change from one genetic state to another over time, influencing tree evaluation in phylogenetics.
UPGMA: UPGMA, or Unweighted Pair Group Method with Arithmetic Mean, is a simple agglomerative clustering method used to construct phylogenetic trees based on distance matrices. It operates by grouping sequences or taxa into clusters based on their average pairwise distances, creating a hierarchical tree structure that reflects the genetic relationships among the sequences.