sackin              package:apTreeshape              R Documentation

_C_o_m_p_u_t_e _t_h_e _S_a_c_k_i_n'_s _i_n_d_e_x _o_f _a _t_r_e_e

_D_e_s_c_r_i_p_t_i_o_n:

     'sackin' computes the Sackin's index on tree and normalizes it.

_U_s_a_g_e:

     sackin(tree, norm = NULL)

_A_r_g_u_m_e_n_t_s:

    tree: An object of class '"treeshape"' on which the Sackin's index
          is computed. 

    norm: A character string equals to '"null"' (default) for no
          normalization, '"pda"' for the PDA normalization or '"yule"'
          for the Yule normalization. 

_D_e_t_a_i_l_s:

     The Sackin's index is computed as the sum of the number of
     ancestors for each tips of the tree. The less balanced a tree is
     and the larger its Sackin's index. It can be normalized in order
     to obtain a statistic that does not depend on the tree size, and
     so compare  trees with different sizes. The normalization depends
     on the reference model (Yule or PDA). Under the Yule model, the
     normalized index is 

                  Iyule = (Is-2*n*sum1/j,j=2..n))/n

     where Is is the non-normalized Sackin's index for a n-tips tree.
     Under the PDA model, the normalized index is 

                          Ipda = Is/ n^(3/2)

     See details on the Colless index.

_V_a_l_u_e:

     An object of class 'numeric' which contains the Sackin's index of
     the tree.

_A_u_t_h_o_r(_s):

     Michael Blum <michael.blum@imag.fr> 
       Nicolas Bortolussi <nicolas.bortolussi@imag.fr> 
      Eric Durand <eric.durand@imag.fr> 
      Olivier Franois <olivier.francois@imag.fr>

_R_e_f_e_r_e_n_c_e_s:

     Mooers, A. O., Heard, S. B. (Mar., 1997) Inferring Evolutionnary
     Process from Phylogenetic Tree Shape. _The Quarterly Review of
     Biology_, *72*, 31 - 54, for more details about the Sackin'index
     and its signification about the balance of phylogenetic trees. 

     Blum, M., Francois, O. and Janson, S. The mean, variance and
     limiting distribution of two statistics sensitive to phylogenetic
     tree balance; manuscript available from 
      <URL: http://www-timc.imag.fr/Olivier.Francois/bfj.pdf>.

_S_e_e _A_l_s_o:

     'colless'
      'sackin.test'

_E_x_a_m_p_l_e_s:

     ## Index of Sackin of a PDA tree :
     tpda<-rtreeshape(1,tip.number=70,model="pda")
     tpda<-tpda[[1]]
     sackin(tpda,norm="pda")
       
     ## Histogram of the Sackin's indices for randomly generated Yule trees, 
     ##      with no normalization
     main="Histogram of Sackin's indices for randomly generated Yule trees"
     xlab="Sackin's index"
     hist(sapply(rtreeshape(300,tip.number=50,model="yule"),FUN=sackin,norm="yule"),
           freq=FALSE, main=main, xlab=xlab)

     ## Change the size of the trees:
     hist(sapply(rtreeshape(300,tip.number=100,model="yule"),FUN=sackin,norm="yule"),
           freq=FALSE, main=main, xlab=xlab)

