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TraitRateProp searched for the following parameters:

--- Phenotypic (character) Model Parameters ---
pi1: the rate of change from state 0 to state 1
mu: a factor to adapt the branch lengths of the tree to the expected number of phenotypic changes per unit time

--- Sequence Model parameters ---
alpha: controls the discrete gamma distribution (4 rate categories) that allows rate variation across sequence sites
kappa: the ratio between the rates of transitions and transversions (HKY85 model)

--- Parameters connecting the trait and sequence evolutionary processes ---
r: the ratio between the rates of sequence evolution in phenotypic state 1 and in phenotypic state 0
p: the proportion of sequence sites in association with the phenotypic trait

--- Additional parameters ---
tree length: the total length of the tree is optimized by shrinking/expanding it up to a factor

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TraitRateProp found the following values for the alternative model:

--- Phenotypic (character) Model Parameters ---
pi1: 0.252772
mu: 9.5282

--- Sequence Model parameters ---
alpha: 0.821783
--- Parameters connecting the trait and sequence evolutionary processes ---
r: 7.60583
p: 0.69937

--- Additional parameters ---
tree length: 1.9748

log-likelihood: -1983.76

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TraitRateProp found the following values for the null model:

--- Phenotypic (character) Model Parameters ---
pi1: 0.720184
mu: 6.11379

--- Sequence Model parameters ---
alpha: 0.821783
--- Parameters connecting the trait and sequence evolutionary processes ---
These parameters are not optimized under the null model

--- Additional parameters ---
tree length: 1.9748

log-likelihood: -2013.44

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Chi-Sq Hypothesis Testing

D statistic is: 59.3600
Degrees of freedom: 2
P-Value is: 1.28870e-13, thus with significance level 0.05 the null hypothesis can be rejected.
An association between the phenotypic trait and the rate of sequence evolution was observed.
The proportion of sites in association with the trait is 0.69937.
The relative rate parameter is 7.60583.

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