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Table 3 Summary of the nine character change models, and the fit of each model to Timema hydrocarbon profiles (represented by DF1 and DF2) and individual hydrocarbon components

From: Hydrocarbon divergence and reproductive isolation in Timemastick insects

Model for trait change

P1

Interpretation

Conclusion if best fit

Profiles

Hydrocarbon components

    

DF1

DF2

3Me27

5Me27

7Me27

9Me27 + 11Me27

13Me27

Pure-Phylogenetic/Distance

1

Time predicts the amount of change occurred (consistent with neutral divergence).

Trait not involved in speciation

2.1

5.6

*

2.1

2.3

2.9

*

Pure-Phylogenetic/Equal

1

The amount of change depends on the number of speciation events occurred (number of nodes).

Consistent with speciational change2

2.0

3.4

0.5

2.4

*

1.7

0.1

Pure-Phylogenetic/Free

16

Trait values can change at any rate between speciation events

Trait not involved in speciation

24.7

27.0

34.9

44.2

40.9

29.0

27.6

Nonphylogenetic/Distance

1

Closely related species share trait values for a short time and then diverge very rapidly

Trait not involved in speciation

8.0

2.0

7.0

*

5.5

1.5

5.4

Nonphylogenetic/Equal

1

Trait values change very rapidly, with similar rates in different lineages

No inference3

5.4

*

4.3

0.1

3.9

*

2.6

Nonphylogenetic/Free

9

Trait values change very rapidly, with different rates in different lineages

No inference3

12.8

14.8

2E+08

2E+08

2E+08

2E+08

2E+08

Punctuated/Distance

1

At each speciation event, one daughter species retains the ancestral trait value, the trait in the other daughter species changes, with the amount of change dependent on time

Consistent with speciational change2, level of divergence between species also affected by the time separating them

1.1

5.0

5.3

14.2

17.3

12.7

6.4

Punctuated/Equal

1

At each speciation event, one daughter species retains the ancestral trait value, the trait in the other daughter species changes, the amount of change between speciation events is always the same

Consistent with speciational change2

*

0.9

5.4

13.9

12.3

9.0

5.3

Punctuated/Free

8

At each speciation event, one daughter species retains the ancestral trait value, the trait in the other daughter species changes, the amount of change between speciation events varies freely

Consistent with speciational change2, level of divergence between species also affected by lineage-specific processes

15.1

19.0

19.3

28.2

31.3

26.7

20.4

  1. Model-fit values are presented as AIC value differences between the focal model and best model (labeled with *). Models that differ by at least 2 AIC units from the best model are considered to provide a significantly worse fit to the data; models within the 2 units are indicated in bold. 3Me27 = 3-methylheptacosane; 5Me27 = 5-methylheptacosane; 7Me27 = 7-methylheptacosane; 9Me27 = 9-methylheptacosane; 11Me27 = 11-methylheptacosane; 13Me27 = 13-methylheptacosane. Notice that the convergent results for 3Me27 and 13Me27 are expected given the strong negative correlation between these two components. 1: Numbers of parameters estimated; see Additional file 1 for details 2: While these models are expected to be the best description for traits involved in speciation, similar phylogenetic patterns may also arise via other processes, for example, when speciation and trait evolution are associated with niche shifts [18]. 3: Support for these models indicates very rapid divergence of traits; however, they do not provide insights into why such rapid divergence occurs (e.g., genetic drift, natural selection).