## FEL-contrast#

HyPhy version required ≥ 2.3.4
Parallel support MP and/or MPI
File path LIB/TemplateBatchFiles/SelectionAnalyses/FEL-contrast.bf
Standard analysis menu Evolutionary Hypothesis Testing > FEL-contrast

### What biological question is the method designed to answer?#

Which sites in a gene may be associated with adaptation to a different environment. You need a tree with branches partitioned (a priori) into two sets: reference and test.

Suppose you have a gene which was sampled from different selective environments. The specific example for which this tool was developed is evolution of HIV in different hosts or different compartments (blood vs brain) in the host. Similar situations arise when the gene is sampled from species living in different environment, eating different food, having different wavelength eye sensitivity. This division has to be binary, however, so that any branch in the tree is either in the reference environment, or the test environment.

FEL-contrast then allows you to examine selective pressures (measured as dN/dS) at each site in the gene individually, and test whether or not they are different between environments.

Armed with a list of such sites, you could then attempt to explore if evolution at these sites is associated with adaptation to the environment.

### What is the statistical procedure and statistical test is used to establish significance for this method?#

For each site, three rates are inferred, with other parameters (frequencies, branch lengths) inferred jointly and held at

• α : synonymous substitution rate
• β r : non-synonymous substitution rate along reference branches
• β p : non-synonymous substitution rate along test branches

Two models are compared using a likelihood ratio test

• HA: α, β r, and β t are inferred by maximum likelihood as free parameters

• H0: The β r := β t constraint is enforced.

The models are nested and differ by one degree of freedom. p-values are computed using the limit χ2 distribution with one degree of freedom.

### How should one interpret positive and negative test results?#

A significant result at a site means that dN/dS (β/&alpha) is different between the two sets of branches, with either an increase or a decrease on the test branches relative to the reference branches. A significant finding does not make any claims about positive (dN/dS > 1) or negative (dN / dS < 1), just that dN/dS differ among sets of branches, i.e., a difference need not change the mode of selection.

Negative results do not mean that there is no difference, rather that whatever difference there may be does not rise to the level of statistical significance/

### Rules of thumb for when this method is likely to work well, and when it is not.#

• Generally, you need 10 or more branches in each set to be able to have any statistical power.
• Too little divergence is also likely to severely throttle statistical power.

### Example#

We will analyze HIV-1 env sequences from a transmission pair: sequences are isolated from the putative source individual and the putative recipient individual from the 2005 study by Frost et al.

1. Partition the tree into the source and recipient (here we include the transmission branch with the source sequences), for example as described here. For convenience, download a NEXUS file with the tree already partitioned.

2. Run HYPHYMP or HYPHYMPI, select Evolutionary Hypothesis Testing from the menu of analyses then select Use a FEL method to test which sites in a gene may be associated with adaptation to a different environment. Alternatively, you can supply the path of the file as a command line argument, e.g. (by default /path/to/hyphylib should be /usr/local/lib/hyphy)

\$HYPHYMP /path/to/hyphylib/TemplateBatchFiles/SelectionAnalyses/FEL-contrast.bf

3. Select Universal genetic code

5. Choose SOURCE as the test set

6. Select Yes to include synonymous rate variation

7. Input 0.1 for the default p-value

The analysis will now run for a few minutes and output the following results

### Branches to use as the test set in the FEL-contrast analysis#

Selected 24 branches to include in FEL calculations: 0564_7, 0564_11, 0564_4, Node6, 0564_1, 0564_21, 0564_5, Node11, Node9, Node5, 0564_17, Node4, 0564_13, 0564_15, Node16, 0564_22, 0564_6, Node20, 0564_3, Node19, Node15, Node3, 0564_9, Node2

### Obtaining branch lengths and nucleotide substitution biases under the nucleotide GTR model#

• Log(L) = -5524.85, AIC-c = 11151.77 (51 estimated parameters)

### Obtaining the global omega estimate based on relative GTR branch lengths and nucleotide substitution biases#

• Log(L) = -5436.84, AIC-c = 10991.98 (59 estimated parameters)
• non-synonymous/synonymous rate ratio for background = 0.9178
• non-synonymous/synonymous rate ratio for test = 0.8293

### Improving branch lengths, nucleotide substitution biases, and global dN/dS ratios under a full codon model#

• Log(L) = -5436.29
• non-synonymous/synonymous rate ratio for background = 1.1136
• non-synonymous/synonymous rate ratio for test = 0.7748

### For partition 1 these sites are significant at p <=0.1#

Codon alpha beta-reference beta-test LRT Difference detected?
4 0.000 22.380 0.000 3.390 Decr. p = 0.0656
52 0.000 20.982 0.000 3.384 Decr. p = 0.0658
83 0.000 20.365 0.000 3.389 Decr. p = 0.0656
118 0.000 17.179 0.000 3.404 Decr. p = 0.0651
124 0.000 23.346 0.000 3.396 Decr. p = 0.0653
155 0.000 0.000 64.943 5.045 Incr. p = 0.0247
187 0.000 20.934 0.000 3.577 Decr. p = 0.0586
218 0.000 20.825 0.000 3.519 Decr. p = 0.0607
222 0.000 22.658 0.000 3.459 Decr. p = 0.0629
224 0.000 25.874 0.000 3.681 Decr. p = 0.0550
352 0.000 19.420 0.000 3.411 Decr. p = 0.0648
386 0.000 20.334 0.000 3.387 Decr. p = 0.0657
417 0.000 21.316 0.000 3.383 Decr. p = 0.0659
455 0.000 22.010 0.000 3.398 Decr. p = 0.0653
462 0.000 69.066 10.567 3.860 Decr. p = 0.0494
466 0.000 55.142 0.000 7.562 Decr. p = 0.0060
506 0.000 33.154 0.000 3.438 Decr. p = 0.0637
526 0.000 50.810 5.313 3.351 Decr. p = 0.0672
533 0.000 21.489 0.000 3.485 Decr. p = 0.0619
598 0.000 18.103 0.000 3.392 Decr. p = 0.0655
633 7.019 20.227 0.000 3.393 Decr. p = 0.0655
748 0.000 36.773 0.000 6.388 Decr. p = 0.0115
751 0.000 18.447 0.000 3.123 Decr. p = 0.0772
762 0.000 18.868 0.000 3.402 Decr. p = 0.0651
788 0.000 26.735 0.000 3.937 Decr. p = 0.0472
820 0.000 56.371 0.000 9.657 Decr. p = 0.0019
824 0.000 19.630 0.000 3.604 Decr. p = 0.0576