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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

Your D statistic is: 59.3600
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

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