dixon2002               package:ecespa               R Documentation

_D_i_x_o_n (_2_0_0_2) _N_e_a_r_e_s_t-_n_e_i_g_h_b_o_r _c_o_n_t_i_n_g_e_n_c_y _t_a_b_l_e _a_n_a_l_y_s_i_s

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

     'dixon2002' is a wrapper to the functions of Dixon (2002) to test
     spatial segregation for several species by analyzing the  counts
     of the nearest neighbour contingency table for a marked point
     pattern.

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

     dixon2002(datos, nsim = 99)

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

   datos: 'data.frame' with three columns: x-coordinate, y-coordinate
          and sp-name. See 'swamp'. 

    nsim: number of simulations for the randomization approximation of
          the p-values. 

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

     A measure of segregation describes the tendency of one species to
     be  associated with itself or with other species. Dixon (2002)
     proposed a measure of the  *segregation of species* _i_ in a
     multiespecies  spatial pattern as:


       S[i] = log{[(N[ii]/(N[i]-N[ii])] / [(N[i]-1)/(N-N[i])]}


     where N[i] is the number of individuals of species _i_, N[ii] is
     the frequency of species _i_ as neighbor of especies _i_ and N is
     the total number of locations.   Values of S[i] larger than 0
     indicate that species _i_ is segregated; the larger the value of
     S[i], the more extreme the segregation.  Values of S[i] less than
     0 indicate that species _i_ is is found as neighbor of itself less
     than expected under random labelling.  Values of S[i] close to 0
     are consistent with random labelling of the neighbors of species
     _i_.

     Dixon (2002) also proposed a *pairwise segregation index* for the
     off-diagonal elements of the contingency table:


       S[ij] = log{[(N[ij]/(N[i]-N[ij])] / [(N[i])/(N-N[j])-1]}


     S[ij] is larger than 0 when N[ij], the frequency of neighbors of
     species _j_ around points of species _i_, is larger than expected
     under random labelling and less than 0 when N[ij] is smaller than
     expected under random labelling.

     As a *species/neighbor-specific test*, Dixon(2002) proposed the
     statistic

                Z[ij] =(N[ij] -EN[ij])/sqrt(Var N[ij])

     where _j_ may be the same as _i_ and EN[ij] is the expected count
     in the contingency table. It has an asymptotic normal distribution
     with mean 0  and variance 1;  its asymptotic p-valure  can be
     obtained from the numerical evaluation of the cumulative normal
     distribution  or by simulation, i.e, by condicting a randomization
     test (appropriate when the sample size is small). 

     An *overall test of random labelling* (i.e. a test that all counts
     in the k x k nearest-neighbor contingency table are equal to their
     expected counts) is based on the quadratic form

                     C = (N-EN)' Sigma^- (N - EN)

     where N is the vector of all cell counts in the contingency table,
     Sigma is the variance-covariance matrix of those counts and
     Sigma^- is a generalized inverse of Sigma. Under the null
     hypothesis of random labelling of points, C  has a asymptotic
     Chi-square distribution with k(k-1)  degrees of freedom (if the
     sample sizes are small its distribution should be estimated using
     Monte-Carlo simulation). P-values are computed from the
     probability of observing equal or larger values of C. The overall
     statistic C can be partitioned into k *species-specific test*
     statistics C[i]. Each C[i] test if the frequencies of the
     neighbors  of species _i_ are similar to the expected frequencies
     if the points were randomly labelled. Because the C[i] are not
     independent Chi-square statistics, they do not sum to the overall
     C.

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

     A list with the following components: 

     ON : Observed nearest neighbor counts in table format. From row sp
          to column sp.  

     EN : Expected nearest neighbor counts in table format.

      Z : Z-score for testing whether the observed count equals the
          expected count.

      S : Segregation measure.

   pZas : P-values based on the asymptotic normal distribution of the Z
          statistic.

    pZr : If nsim !=0, p-values of the Z-score based on the
          randomization distribution.

      C : Overall test of random labelling.

     Ci : Species-specific test of random labelling.

   pCas : P-value of the overall test from the asymptotic chi-square
          distribution with the appropriate degrees of freedom.

  pCias : P-values of the species-specific tests from the asymptotic
          chi-square distribution with the appropriate degrees of
          freedom.

    pCr : If nsim !=0, p-value of the overall test from the
          randomization distribution.

   pCir : If nsim !=0, p-values of the species-specific tests from the
          randomization distribution.

 tablaZ : table with ON, EN, Z, S, pZas and pZr in pretty format, as in
          the table II of Dixon (2002).

 tablaC : table with C, Ci, pCas,pCias, pCr and pCir  in pretty format,
          as in the table IV of Dixon (2002).

_W_a_r_n_i_n_g:

     The S[i] and S[ij] statistics asume that the spatial
     nearest-neighbor process is stationary, at least to second order, 
     i.e., have the same sign in every part of the entire plot. A
     biologically heterogeneous process will violate this asumption.

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

     Philip M. Dixon <URL: http://www.public.iastate.edu/~pdixon/>.
     Marcelino de la Cruz marcelino.delacruz@upm.es wrote the wrapper
     code  for the 'ecespa' version.

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

     Dixon, P.M. 2002. Nearest-neighbor  contingency table analysis of
     spatial segregation for several species. _Ecoscience_, *9* (2):
     142-151.

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

     'K012' for another segregation test, based in the differences of
     univariate and bivariate K-functions.

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

     ## Not run: 

     data(swamp)

     dixon2002(swamp,nsim=99)

     ## End(Not run)

