K012             package:ecespa             R Documentation(latin1)

_T_e_s_t_s _a_g_a_i_n_s_t '_i_n_d_e_p_e_n_d_e_n_t _l_a_b_e_l_l_i_n_g'

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

     Given a "fixed" point pattern and some process that asign labels
     (I,J) to another "variable" point pattern, 'K012' estimates the
     combined bivariate K function between the fixed pattern and every
     type of the  variable pattern, and  test that they are independent
     (i.e. that the labels are randomly assigned, irrespectively of the
     fixed pattern).

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

     K012(X, fijo, i, j, nsim = 99, nrank = 1, r = NULL,
              correction = "isotropic")

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

       X: Multitype marked point pattern. An object with the 'ppp'
          format of 'spatstat'.   

    fijo: Number or character string identifying the mark value of the 
          "fixed" pattern in X 

       i: Number or character string identifying the mark value of the 
          I pattern in X 

       j: Number or character string identifying the mark value of the 
          J pattern in X 

    nsim: Number of simulated point patterns to be generated when
          computing the envelopes.

   nrank: Integer. Rank of the envelope value amongst the 'nsim'
          simulated values.  A rank of 1 means that the minimum and
          maximum simulated values will be used. 

       r: Numeric vector. The values of the argument r at which the K
          functions  should be evaluated. 

correction: A character item selecting any of the options "border",
          "bord.modif", "isotropic", "Ripley" or "translate". It
          specifies the edge correction(s) to be applied. 

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

     This test was developped to answer some questions about the
     spatial pattern of survival and mortality of seedlings and its
     relationships with adult plants in a plant community (De la Cruz
     _et al. In press_ ). In order to evaluate the spatial structures
     of seedlings fates (survive or die), the null hypothesis of random
     labelling (Cuzick & Edwards 1990, Dixon 2002) would be the
     appropriate one. This kind of pattern is the result of two
     hierarchical processes: a first one that generates the pattern of
     points (seedlings) and other that assign "labels" (i.e. "die",
     "survive") to the points. On the other hand,  to analyze the
     relationships between the spatial pattern of  emerging seedlings
     and the pattern of adult plants (two patterns that have been
     generated independently), independence would be the appropriate
     null hypothesis (Goreaud & Pellisier 2003). However, testing the
     relationship between the pattern of seedling fates and the pattern
     of adult plants does not completely fit any of the  mentioned
     hypotheses because, although the pattern of adult plants and the
     pattern of, e.g., dead seedlings are generated independently,
     their relationship is conditioned by the dependence of the fate
     "dead" on the locations of emerging seedlings. This implies that 
     one can not apply the usual technique of toroidal shifting one
     pattern over the other to test the independence hypothesis.
     Instead one must permute the label of the focal fate (i.e.
     survive, die) over the global pattern of seedlings points, keeping
     the locations and labels of adults fixed. This is the method that
     'K012' uses to build the envelopes. The bivariate K functions are
     computed with the Lotwick's and Silverman's (1982) combined
     estimator ('Kmulti.ls').

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

     A list with two elements. 

    k01 : Bivariate K function of the fixed point pattern and the I
          variable type, with simulation envelopes

    k02 : Bivariate K function of the fixed point pattern and the J
          variable type, with simulation envelopes

        : 

        : Each of the above elements is a 'fv.object', essentially a
          'data.frame' with the following items: 

      r : the values of the argument r at which the functions kave been
          estimated

     hi : upper envelope of simulations

     lo : lower envelope of simulations

     together with the observed corrected estimate of the combined
     bivariate K function ( 'iso', 'trans', 'border', etc).

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

     Marcelino de la Cruz marcelino.delacruz@upm.es

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

     Cuzick, J. and Edwards, R. 1990. Spatial clustering for
     inhomogeneous populations (with discussion).  _Journal of the
     Royal Statistical Society_ B * 52*: 73-104.

     De la Cruz, M. 2006. Introduccion al analisis  de datos mapeados o
     algunas de las (muchas) cosas  que puedo hacer si tengo
     coordenadas. _Ecosistemas_ 15 (3): 19-39.  <URL:
     http://www.revistaecosistemas.net/pdfs/448.pdf>.

     De la Cruz, M., Romao, R.L., Escudero, A. & Maestre, F.T.  _In
     press_. Where do seedlings go? A spatio-temporal analysis of early
     mortality in a semiarid specialist. _Ecography_.

     Dixon, P. M. 2002. Ripley's K function. In _The encyclopedia of
     environmetrics_  (eds. El-Shaarawi, A.H. & Piergorsch, W.W.), pp.
     1976-1803. John Wiley & Sons Ltd, NY.

     Goreaud, F. and Pelissier, R. 2003. Avoiding misinterpretation of
     biotic interactions with the intertype K12-function: population
     independence  vs. random labelling hypotheses. _J. Veg. Sci._
     *14*: 681-692.

     Lotwick, H. W. & Silverman, B. W. 1982. Methods for analysing
     spatial processes of several types of points.  _Journal of the
     Royal Statistical Society_ B *44*: 406-413.

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

     'dixon2002' for another segregation test, based in the contingency
     table of counts of nearest neigbors in a marked point pattern.

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

     ## Not run: 

     data(Helianthemum)

     ## Test asociation/repulsion between the fixed pattern of adult
     ## H. squamatum plants and the "variable" pattern of surviving and 
     ## dead seedlings, with 2.5% and 97.5% envelopes of 999 random 
     ## labellings.

     cosa <- K012(Helianthemum, fijo="adultHS", i="deadpl", j="survpl",
                  r=seq(0,200,le=201), nsim=999, nrank=25, correction="isotropic")

     plot(cosa$k01, sqrt(./pi)-r~r,  col=c(3, 1, 3), lty=c(3, 1, 3), las=1,
              ylab=expression(L[12]), xlim=c(0, 200), 
              main="adult HS vs. dead seedlings")

     plot(cosa$k02, sqrt(./pi)-r~r, col=c(3, 1, 3), lty=c(3, 1, 3), las=1, 
              ylab=expression(L[12]), xlim=c(0, 200),
              main="adult HS vs. surviving seedlings")
     ## End(Not run)

