Concatenation A complicated story Concatenated ML Assumes all - - PowerPoint PPT Presentation

Concatenation

A complicated story

Concatenated ML

• Assumes all sequences evolve down 1 tree
• As mutation rate -> 0
• Likelihood dominated by single mutations
• When a character changes, it changes once
• Maximum Likelihood -> Maximum Parsimony
• This is Claim 1

Proposition 1

The six-leaf balanced tree has a lower parsimony score than the unbalanced tree

• As branches shorten, deep coalescence ‘almost

always’

Conditions

• Concatenated ML is inconsistent for certain

caterpillar trees

• Our intuition is that this is all species trees n>6
• This proof covers caterpillar species trees n=6
• However, the mutation rate must be very low
• r-state symmetric and infinite alleles equivalent
• Gets worse as you add genes/sites

Partitioned ML

• What makes it partitioned?
• Only assume constant topology
• Branch lengths + substitution matrices can

vary

• Statistically consistent under ILS?
• Not affected by this proof, so maybe?

PANIC

• Unpartitioned ML positively misleading
• All results for statistical consistency of summary

methods assumes infinite length genes

• No gene tree error
• In the presence of gene tree error: ?!?!
• In the presence of recombination: ?!?!
• No method proven consistent on fixed-length genes

Keep Calm, Concatenate

• short edges -> concatenated alignments fail
• Extinction -> few short edges deep in tree
• Failures probably restricted to twigs
• Real data->few deep short edges
• But how would you know?

Now what?

• Good news:
• The species tree is identifiable
• A statistically consistent method is possible
• Bad news:
• Either don’t have it or can’t prove we have it
• Good news again:
• Concatenation works ok, I guess

Questions?