2.1 Historical biogeographical analyses
The ancestral ranges of the Galliformes group were estimated by utilizing the well-established phylogenetic tree for 197 Galliformes (Hugall and Stuart-Fox, ). The following terrestrial regions are considered in biogeographical analyses: East Asia (A), South Asia (B), Southeast Asia (C), West Asia (D), North America (E), South America (F), Africa (G), Europe (H) and Oceania (I). Distribution of each species over these terrestrial regions was obtained from the Avibase database (http://avibase.bsc-eoc.org/avibase.jsp?lang=EN).
In comparing ancestral ranges of Galliformes species, three analytical methods are used, i.e.,dispersal-vicariance analysis (DIVA), Bayesian binary MCMC analysis (BBM) and dispersal-extinction-cladogenesis analysis (DEC). All three methods are carried out by using the software RASP (Yu et al., , ).
2.2 Temporal analyses of rates of diversification
Different diversification rate-shifting models have been tried to fit the Galliformes phylogeny, as proposed in previous studies (Rabosky, [2006b]; Rabosky and Lovette, [2008a], [2008b]). Specifically, four methods from an R package “laser” (Rabosky, [2006a]) are implemented for comparative purposes, consisting of a constant-speciation and constant-extinction model (CONSTANT), a decreasing-speciation and constant-extinction model (SPVAR), a constant-speciation and increasing-extinction model (EXVAR) and a decreasing-speciation and increasing-extinction model (BOTHVAR) (Chen, ). These four models have been used to test the temporal shifting patterns in rates of diversification of different taxa (Rabosky and Lovette, [2008a], [2008b]).
Each of the models require four parameters for estimation (Rabosky and Lovette, [2008b]), which can be obtained by maximizing the following likelihood equation (Rabosky, [2006b]):
where t is the vector of observed branch times from the phylogeny, t
the branch time for the lineage, while n, λ(t) and μ(t) are time-dependent speciation and extinction rates, respectively. The time-dependent rate of diversification is defined as r(t) = λ(t) − μ(t) and N is the number of external tips in the tree.
In the CONSTANT model, λ(t) and μ(t) are assumed to be constant over the entire phylogenetic tree (i.e., λ(t) = λ
0, μ(t) = μ
0), where λ
0 and μ
0 are the constants to be estimated. In the SPVAR model, μ(t) is assumed to be constant over the entire tree (i.e., μ(t) = μ
0), while λ(t) is assumed to decrease continuously from the root to the tips of the tree, defined as follows: λ(t) = λ
0 exp(−kt). As seen in the SPVAR model, the additional parameter k is required to model the declining trend of rate of speciation over the tree. For this model, the rate of diversification is predicted to decline over the evolutionary time as (r(t) = λ
0 exp(−kt) − μ
0). In the EXVAR model, the rate of speciation is assumed to be constant over the tree while the rate of extinction is assumed to decline over the tree as follows: u(t) = u
0(1 − exp(−zt)). As well, this model has an additional parameter, i.e., z, to be estimated. Finally, in the BOTHVAR model, both λ(t) and μ(t) are assumed to change over time as follows: λ(t) = λ
0 exp(−kt) and u(t) = u
0(1 − exp(−zt)) (Rabosky, [2006b]; Rabosky and Lovette, [2008b]).
2.3 Clade age and clade richness relationships
The evolutionary age for each clade is calculated as the phylogenetic distance between the root and the internal node leading to the focused clade. The corresponding clade species richness is defined as the number of external tips (living species) for that specific clade.
To reveal the possible relationship between clade age and clade species richness and/or phylogenetic diversity, I performed both a non-phylogenetic ordinary least-squares regression analysis (OLS) and a phylogenetic general least-squares regression analysis (PGLS). Given that various clades are not independent from each other, it is necessary to remove the impacts of phylogenetic inertia by performing PGLS, i.e., a method to introduce a phylogenetic variance-covariance matrix in the fitting formula, a matrix missing in the OLS method. For the OLS method, the vector of coefficients is fitted using the following identity:
while for the PGLS method, the vector of coefficients is estimated from the following equation:
The superscript T denotes the transpose of a matrix, while −1 denotes the inverse of a matrix. X is a matrix with columns indicating the explanatory variables, while y is a column vector storing the values for the response variable and W is the phylogenetic variance-covariance matrix. The calculation of W is only related to the branch lengths of the phylogenetic tree (Revell, ).