K1K2             package:ecespa             R Documentation(latin1)

_D_i_f_f_e_r_e_n_c_e_s _b_e_t_w_e_e_n _u_n_i_v_a_r_i_a_t_e _a_n_d _b_i_v_a_r_i_a_t_e _K-_f_u_n_c_t_i_o_n_s

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

     Given two point patterns I and J, 'K1K2'computes the differences
     between  both univariate K-functions (i.e. Ki(r)-Kj(r)) as well as
     the differences between  the univariate and the bivariate
     K-function (i.e. Ki(r)-Kij(r) and Kj(r)-Kij(r)). It also computes
     simulation envelopes to test  that that the observed differences
     are within the  range expected asuming the random labelling
     hypothesis.

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

     K1K2(X, 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'.  

       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(r) 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:

     The indiscriminate use of the raw bivariate functions (mainly the
     K or the L-bivariate functions) in ecological studies for testing
     the association/ repulsion between different point patterns waste
     some of the most interesting properties of the K-function. One of
     them is that under the random labelling hypothesis every
     individual pattern would be a random thinning of the corresponding
     bivariate pattern and therefore Ki(r)=Kj(r)= Kij(r)=pi*r^2 (Diggle
     2003).  Dixon (2002) sugested that some differences of these
     functions could provide provide interesting ecological
     information. For example, Ki(r)-Kj(r), has an expected value of 0
     for all r distances under random labelling and evaluates the
     differences in the intensity of aggregation of the two point
     patterns (e.g., in the example bellow, the pattern of drought and
     herbivory deaths). Other relevant function is Ki(r)-Kij(r) and the
     complementary Kj(r)-Kij(r) which evaluate the degree of
     segregation of every individual pattern, i.e. if every point of
     the pattern is more -or less- surrounded by other points of the
     same type than would be expected under the random labelling
     hypothesis. 'K1K2' uses K^*ij(r), the combined estimator of
     Lotwick and Silverman (a weigthed mean of  Kij(r)  and Kji(r)) as
     computed by 'Kmulti.ls'.

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

     A list with three elements. 

   k1k2 : Difference between Ki(r) and Kj(r), with simulation
          envelopes.

  k1k12 : Difference between Ki(r) and Kij(r), with simulation
          envelopes.

  k2k12 : Difference between Kj(r) and Kij(r), 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 difference in each case (respectively
     'K1-K2', 'K1-K12' and 'K2-K12').

_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:

     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. and Maestre, F.T. 2008.
     Where do seedlings go? A spatio-temporal analysis of early
     mortality in a semiarid specialist. _Ecography_,31 DOI:
     10.1111/j.2008.0906-7590.05299 .

     Diggle, P.J. 2003. _Statistical analysis of spatial point
     patterns_. Arnold, London.

     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.

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

     ## Not run: 
     data(Helianthemum)

     cosa12 <- K1K2(Helianthemum, j="deadpl", i="survpl", r=seq(0,200,le=201),
                      nsim=999, nrank=1, correction="isotropic")

     plot(cosa12$k1k2, lty=c(2, 1, 2), col=c(2, 1, 2), xlim=c(0, 200),
              main= "survival- death")

     plot(cosa12$k1k12, lty=c(2, 1, 2), col=c(2, 1, 2), xlim=c(0, 200),
              main="segregation of surviving seedlings")

     plot(cosa12$k2k12, lty=c(2, 1, 2), col=c(2, 1, 2), xlim=c(0, 200),
              main= "segregation of dying seedlings")
     ## End(Not run)

