Performs linear regression between phylogenetic independent contrasts (PICs) of tip rates and continuous trais

```
TipCorrelation(phy, tip.rate, trait, log=TRUE, remove.cherries=TRUE,
scaled=TRUE, positivise=TRUE, use.lmorigin=TRUE)
```

## Arguments

- phy
an ultrametric phylogenetic tree of class 'phylo'.

- tip.rate
an object of class 'named numeric' containing tip.rates

- trait
an object of class 'named numeric' containing continuous trait data

- log
Should tip.rate and trait values be logged before regression? The default is TRUE.

- remove.cherries
Should PICs of 'cherries' be pruned before regression? The default is TRUE.

- scaled
Should PICs be scaled with their expected variances? The default to TRUE.

- positivise
Should PICs be positivised before regression? The default is TRUE.

- use.lmorigin
Should a regression-through-origin be performed instead of regular linear model? The default is TRUE.

## Details

Tip rates as those obtained with `MiSSEGreedy`

are analogous to a continuous trait evolving in the tree and must also be corrected for phylogenetic
non-independence before regression analyses. This function does that by using PICs (Felsenstein, 1985) and gives the additional option of removing PICs
from 'cherries' from analyses. Cherries (theoretically) inherit the exact same rate class probabilities in any model that uses just branch lengths to estimate
tip rates. For that reason, they may: (1) present identical tip rates, forcing the slope of the regression to be close to 0 since all PICs for cherries will be 0;
and (2) constitute pseudoreplicates in the analyses. We suspect that, for that reason, it may make sense to prune them out from any PIC analyses that uses tip-rate
correlations from tree-only diversification approaches (see Vasconcelos et al. in prep.).

## Value

Returns an object that contains:

- $correlation
summary of correlation results.

- $tip.rate PIC
tip rate PICs for each node.

- $trait PIC
trait PICs for each node.

## References

Vasconcelos, T, B.C. O'Meara, and J.M. Beaulieu. In prep.
Felsenstein, J. (1985). Phylogenies and the comparative method. The American Naturalist, 125, 1-15.

## Author

Thais Vasconcelos and Brian O'Meara