"if scientists are going to use logically unbeatable theories about the world, they might as well give up natural science and take up religion (Lewontin, 1972)"

Part I:
Practice with Character State Reconstructions

Transformations among character states may be either accelerated or delayed.  If accelerated, changes among states happen earlier on the tree rather than later and the numbers of reversals are increased.  If delayed, the state changes occur later on the tree and independent gains increase.

What two biological processes do these different modes of character evolution correspond to?

These different reconstructions are referred to as ACCTRAN and DELTRAN in both Macclade and PAUP.

1) Open the file ³DELTRAN/ACCTRAN example² in your Macclade examples.

There are 64 equally parsimonious reconstructions of character evolution for this character.  If we are interested in the number of changes from wrinkled (state 2) to smooth (state 0) texture, then we might think to ignore most of these resolutions, and examine just the DELTRAN and ACCTRAN resolutions, hoping that these would provide extreme values for the number of wrinkled -> smooth changes.

2) Under ³Trace² click on ³resolving options.² This provides you with the option of choosing either ACCTRAN or DELTRAN

3) Choose DELTRAN and examine the reconstructions and then repeat for ACCTRAN.

4) How do these reconstructions differ?

DELTRAN:  1 resolution, which displays 0 changes from wrinkled -> smooth.

ACCTRAN: 2 resolutions, which both display 0 changes from wrinkled -> smooth.

5) now turn on equivocal cycling (which will find in turn each of the most parsimonious reconstructions for the characters of interest). To do this go again to ³Trace² and click on Equivocal cycling.  Now you may use the ³butterfly-R² keystroke to pass your way through each of the possible character state reconstructions.

6) How many possible (equally most-parsimonious) reconstructions exist?

7) Using the ³Go-To² option, go to tree reconstruction number 64.  How many changes from - wrinkled                            smooth ?

8) examine the differences between the first and the last reconstructions (of all possible, attained using equivocal cycling) for the character under examination.  These are MINSTATE and MAXSTATE,  respectively.

9) Now consider this:  Which reconstructions should you prefer Min/Max/Deltran/Acctran?  [there is no right or wrong answer here, but try to think in terms of your own interest and decide what you would reconstructions you would prefer to examine given a particular null hypothesis]

now that we know a bit about character state reconstructions and what assumptions determine our choices, letıs now begin to ask questions about the statistical significance of character evolutions (that is, character evolution)

Part II:
Patterns of Correlated Character Evolution

A Brief Description of the Test
The concentrated-changes test of Maddison (1990) is designed for testing the association of changes in a binary character with some other binary variable within a clade of interest. It can test whether changes (from 0 to 1) in one (dependent) character are more concentrated than expected by chance on branches having a shared character state  for another (independent) character.

Example:  How to implement the concentrated-changes test (Maddisonıs test)

1) Under Macclade examples open the file ³Concentrated Changes Example²

2) Note that there are two characters included.  Tree upon which these characters will be mapped has already been created. The reconstruction is robust.

3) Go to data editor and using ³State Names² rename each of the two characters and states in the following way.

a. character 1 = dependent character Fruit type;  states: 0=fleshy, ancestral;  1= dry, derived
b. character 2 = independent character Ecology; states 0= tropical rainforest; 1= open Savanna

4) Count the number of times dry fruits have evolved from fleshy across this phylogeny of Plants.

5) Now examine their Ecology and note that all instances of dry fruits occur within clades inhabiting open Savannas.

6) This may suggest something about the causal influences of Ecology on Fruit type, but we must test this relationship for statistical significance. Are the changes in fruit type from fleshy to dry ³overly² concentrated in those clades inhabiting open savannas?

To test this we must first establish our null hypothesis-- Write down that  hypothesis here:

7) Our question now becomes: What is the probability, given the above null hypothesis, that the three gains of dry fruits from fleshy would occur in clades inhabiting grasslands?

8) Pull your tools out to the tree window and click on the ³Character-correlation tool² (the tree with the ³c² at its base)

9) In the dialog box that comes up (called the Correlation Test Parameters dialog box) add in the number of gains and losses of the dry fruits.

10) Now click on ³exact count²-- This will use the formulae presented by Maddison, 1990 (a must-read).  The ³exact count² algorithms become computationally difficult as one increases the number of changes in the dependent variable of interest (in fact, changes in the dependent character of more than say 5 or 6 can take a long time), doing simulations can be reasonable and often necessary option.  The simulations generate changes randomly on the clade selected and counts the numbers of gains and losses within the branches specified as the independent variable as well as across the entire tree.  Only those that correspond to the previously specified number of gains and losses will be examined for the branch-distributions of gains and losses. (See below for an example of a simulation output.)

11) Now click on ³Calculate²

12) The next dialog box that will appear is the Correlation Test Results Dialog Box which will allow you to ask what the probability is of having more, as many, or fewer than the indicated number of gains and losses along the distinguished branches (independent variable branches)

13) Find out the probability of having as many as or more than three gains and zero losses and write down that probability here:

14) What can we say about the evolution of dry fruits in Savannas???

15) What are the assumptions of the Maddisonıs Test?



Results from concentrated-changes correlation test
MacClade version 3.01

Data file: Concentrated Changes Example.
Character traced: 2
Current tree: a tree.

Calculated by SIMULATION of MINSTATE-reconstructed changes
 with total sample size 1000
Initial state in simulation at basal node of clade chosen is 0
Compensation: 1

Probabilities of observing various numbers of
gains and losses on branches distinguished by state 1 in character traced,
given 3 gains and 0 losses reconstructed over whole clade,

given state 0 reconstructed at ancestral node of clade:
Sample size: 1000
Gains Losses 0
0  0.087000
1  0.391000
2  0.417000
3  0.105000

given state 1 reconstructed at ancestral node of clade:
Sample size: 0
Gains Losses 0
0  0.0
1  0.0
2  0.0
3  0.0

given either state 0 or 1 reconstructed at ancestral node of clade:
Sample size: 1000
Gains Losses 0
0  0.087000
1  0.391000
2  0.417000
3  0.105000

Report on total number of changes assigned to each node during simulation.
This can be used as a check that changes were assigned uniformly
(but note that root of clade receives no changes).