Mathematics

A Mathematical Primer of Molecular Phylogenetics
Xuhua Xia, PhD

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A Mathematical Primer of Molecular Phylogenetics

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This forthcoming volume offers a unique perspective on a number of phylogenetic issues that have not been covered in detail in previous publications. The volume will provide sufficient mathematical background for young mathematicians and computational scientists, as well as mathematically inclined biology students, to make a smooth entry into the expanding field of molecular phylogenetics. The book will also provide sufficient details for researchers in phylogenetics to understand the workings of existing software packages used in phylogenetics.

The volume offers comprehensive but detailed numerical illustration to render difficult mathematical and computational concepts in molecular phylogenetics accessible to a variety of readers with different academic background.

The text will include examples of solved problems after each chapter, which will be particularly helpful for fourth-year undergraduates, postgraduates, postdocs in biology, mathematics and computer sciences. Researchers in molecular biology and evolution will find it very informative as well.

CONTENTS:
Tentative content
Chapter 1: Introduction to molecular phylogenetics
1. Molecular markers in animal and human forensics
2. Is there a universal yard-stick in molecular phylogenetics?
3. Microevolution and macroevolution
4. The two key objectives of molecular phylogenetics: ancestor-descendent relationships and dating speciation and gene-duplication events
5. General approaches to molecular phylogenetics
6. In phylogenetics, dependent variable is sequence variation and independent variables are substitution model, tree topology and tree branch lengths
7. Gene trees and species tree: approaches to estimating the latter
8. Application of molecular phylogenetics
Chapter 2: Sequence Alignment
1. Sequence alignment is for inferring site homology
2. Scandalous sequence alignments published in phylogenetic literature
3. Which alignment is the best: scoring schemes and alignment scores
4. Dynamic programming: Pairwise alignment with constant gap penalty
5. Dynamic programming: Pairwise alignment with affine function gap penalty
6. Nucleotide and amino acid substitution matrices
7. Pairwise alignment between sequences 1 and 2, 1 and 3 and 2 and 3 can contradict each other in homology identification
8. Aligning very long sequences: use fast heuristic local alignment to break long sequences into segments
9. Progressive multiple alignment: profile or reconstructed sequence for internal node?
10. Alternative multiple alignment methods
11. Automated post-alignment adjustment for nucleotide and amino acid sequences
12. Sequence alignment with secondary structure
13. Align nucleotide sequences against aligned amino acid sequences
14. Align codon sequences and automated post-alignment adjustment
Chapter 3: Markov chain and substitution models
1. Multiple substitutions, when uncorrected, lead to biased phylogenetic estimation
2. Fundamentals of Markov chain
1. Biological basis of different substitution rates
2. Rate heterogeneity over sites and among lineages
3. Substitution models for nucleotide, amino acid and codon sequences
4. Choose the best model: likelihood ratio test and information-theoretic indices
5. The consequence of an over-fitting substitution model: topology becomes irrelevant
Chapter 4: Distance-based phylogenetic methods
1. Model-based evolutionary distances
2. Independent estimation and simultaneous estimation of evolutionary distances
3. Tree-building algorithms for distance matrices
4. Constrained optimization with non-negative branch lengths
5. Branch-and-bound search in least-squares-based method
6. Distance-based statistical tests of alternative topologies
7. Phylogenetics with only pairwise alignment
8. Strengths and weaknesses of distance-based methods
Chapter 5: Maximum parsimony methods in phylogenetics
1. Dynamic programming and Fitch algorithm: uses only informative sites and assumes equal substitution rates
2. Dynamic programming and Sankoff algorithm: goes beyond informative sites and allows differential substitution rates
3. Branch-and-bound search in parsimony method
4. Statistical tests of alternative topologies
Chapter 6: Likelihood methods in phylogenetics
1. Likelihood philosophy: All statistical inferences should be based on data and data only
2. Dynamic programming and the pruning algorithm: Likelihood calculations
3. Likelihood calculations in phylogenetics with missing data and potential bias
4. Branch and bound search in the likelihood approach
5. Testing alternative phylogenetic hypotheses
6. Likelihood ratio tests in phylogenetics
Chapter 7: Bayesian inference in phylogenetics
1. Cases where a rough guess is better or worse than no guess
2. Computational difficulties with the conventional Bayesian approach
3. Markov chain Monte Carlo method
4. Bayesian MCMC
5. Do we need Bayesian inferences when we have a lot of data?
6. The pros and cons of Bayesian inference with parameter-rich models
7. Potential bias in Bayesian phylogenetic reconstruction
Chapter 8: Phylogenetics without sequence alignment
1. When homologous sequences cannot be found (A virus needs 10 functions/structures to survive but different viruses use non-homologous sequences to perform each of the 10 functions/structures)
2. Sharing of ancestral peptides
3. Sharing of DNA morphology: palindromes
4. Other protein and DNA phenotypes
5. Trees based on protein and DNA phenotypic similarities
6. Application in viral taxonomy
Chapter 9: Molecular clock and dating of evolution events
1. Biological insights gained from dating evolutionary events
2. Dating speciation and gene duplication events
3. Relative-rate tests
4. Tree-based tests of molecular clock: distance-based and likelihood-based methods
5. Dating methods
Chapter 10: Phylogeny-based comparative methods
1. Why phylogeny is important in inferring relationships of biological variables sampled from different species
2. Likelihood approaches to characterize associations between binary variables (e.g., gene presence/absence)
3. Likelihood approaches involving variables with more than two states
4. Likelihood approaches involving continuous variables
5. Detecting site dependence in nucleotide and amino acid sequences
Chapter 11: Detecting horizontal gene transfer
1. Horizontal gene transfer in bacterial species
2. Phylogenetic incongruence test
3. Towards a substitution model of gene gain/loss
Chapter 12: Phylogenomics
1. Detecting sequence conservation of non-coding sequences
2. Large-scale phylogeny-based gene association studies
Chapter 13: Molecular phylogenetics and evolution
1. Evolution of bacteriophage and plasmids to their host translation machinery
2. Evolution of splice sites in response to the selection imposed by the splicing machinery
3. Evolution of Helicobacter pylori in the acidic gastric environment
Chapter 14: Molecular phylogenetics and coevolution
1. Coevolution between Shine-Dalgarno (SD) sequences and anti-SD sequences in bacteria
2. Coevolution between peptide chain release factors and translation termination motifs


About the Authors / Editors:
Xuhua Xia, PhD
Professor, Biology Department, University of Ottawa, Ontario, Canada




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