The phrase "a free rate" is correct and usable in written English.
It can be used in contexts related to finance, pricing, or services where no charge is applied.
Example: "The bank offers a free rate for new customers during their first year of service."
Alternatives: "no-cost rate" or "complimentary rate".
Monetary unit: tugrik, with (Oct . 7 , 1994a free rate of 400 tugrik to U.S. $1 6366 tugrik = £11 sterling).
Monetary unit: karbovanets (Ukrainian coupon), with (Oct . 7 , 1994a free rate of 30,028 karbovantsy = U.S. $1 47,7600 karbovantsy = £1 sterling).
Monetary unit: New (Israeli) sheqel, with (Oct . 11 , 1996a free rate of 3.19 sheqalim to U.S. $1 5.033 sheqalim = £1 sterling).
Monetary unit: Belarusian rubel, with (Oct . 7 , 1994a free rate of 5,854 rubels = U.S. $1 9,3122 rubels = £11 sterling).
Monetary unit: hryvnia (a new currency introduced Sept. 2, 1996, to replace the karbovanets at a rate of 1 hryvnia = 100,000 karbovantsy; on September 16 the hryvnia became sole legal tender), with (Oct . 11 , 1996a free rate of 1.77 hryvny to U.S. $1 2.788 hryvny = £1 sterling).
Third, to account for potential heterotachy, we derived ML trees with a free rates parameter covarion model recently implemented in PhyML.
To do this, we estimated the likelihoods of both a constant rates model and a free rates model (where there is one rate per branch) in the program HyPhy v2.1 [ 83], and compared them using a likelihood ratio test.
In addition, we also fitted a free rates (FR) model that takes into account GD heterogeneity across gene families using two discrete Γ distributions with two categories (GD-FR-ML+dG2).
For two of our alignments (mitochondrial shallow, nuclear metatherian), an equal-rate model had significantly better fit to the data over a free-rate model.
Details of the Z-tests are included in Additional File 5. A free-rate model, where a separate substitution rate was estimated for each branch, had significantly better fit to the data for 4 of our 6 alignments, over an equal-rate mode where terminal branches within a pair had equal substitution rates.
We compared the likelihoods of two models: an equal-rate model, where terminal branches within a pair are constrained to have equal substitution rates, but substitution rates are allowed to vary between pairs; and a free-rate model, where a separate substitution rate is estimated for each terminal branch.
