Some blog posts discussing the technical aspects of constructing phylogenetic networks

A fundamental limitation of hybridization networks?
A fundamental limitation of hybridization networks? (2)
How should we treat hybrids in a taxonomic scheme?
Monophyletic groups in networks

Can networks have multiple roots?
Time inconsistency in evolutionary networks
Networks and most recent common ancestors
Is rate variation among lineages actually due to reticulation?
Reconstructing ancestors in a splits network?

Another phylogenetic network outside science
The phylogenetics of Little Red Riding Hood
Roots and the phylogenetics of mythology
Candy Crush network

Validating methods for constructing evolutionary phylogenetic networks
What should a database of datasets look like?
GPWG Poaceae dataset
Datasets for validating algorithms for evolutionary networks

Biological versus phylogenetic networks
Network measures and phylogenetic networks
Trees, treemaps and networks

Are mathematical constraints biologically realistic?
Different topological restrictions of rooted phylogenetic networks. Which make biological sense?
Topological restrictions: some comments

Reviews of recent books
Report from conference Mathematical and Computational Evolutionary Biology 2013 (MCEB 2013)

An update on level-k phylogenetic networks
New version of phylogenetic networks software

Networks and bootstraps as tree-support criteria
Rooted networks for exploratory data analysis
When is there support for a large phylogeny?

Human races, networks and fuzzy clusters
Admixture graphs – evolutionary networks for population biology
Using phylogenetic analyses for textual analysis

Open questions about evolutionary networks, part 1
Open questions about evolutionary networks, part 2
Open questions about evolutionary networks, part 3
An open question about computational complexity
Using constraints to get a handle on the space of phylogenetic networks?
Phylogenetic network Millennium problems

EDA or post-optimality analysis of phylogenetic data?
Some possible questions for EDA in phylogenetics
Representing evolutionary scenarios using splits graphs

Are phylogenetic networks as scientific as trees?
Description, explanation and prediction in phylogenetics
Is there a philosophy of phylogenetic networks?

Are phylogenetic trees useful for domesticated organisms?
Networks and human inter-population variation
Network of apple cultivars
The phylogenetics of angiosperm classification schemes

Distortions and artifacts in Principal Components Analysis analysis of genome data
Networks can outperform PCA ordinations in phylogenetic analysis
Pacific rock art - ordinations and networks
Phylogenetic networks as multivariate data displays

We should present bayesian phylogenetic analyses using networks
Cloudograms and data-display networks
Pasta have no phylogeny (so don't try to give them one)
Should phylogenetic modelling proceed from simple to complex or vice versa?

Resistance to network thinking
Destroying the Tree of Life?
A rant about the term "evolutionary network"
Phylogenetic networks and "evolutionary networks"

First-degree relationships and partly directed networks
Cophylogenetic networks

Conflicting placental roots: network or tree?
Why are there conflicting placental roots?

Checking data errors with phylogenetic networks
Multivariate data displays are not always necessary

Barcodes, metaphors, and phylogenetic networks
Next Generation Sequencing and phylogenetic networks
Phylogenetics, ecologist style
The Phylocode and reticulation

Evolution and timelines
Non-phylogenetic trees

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