dixon2002 | R Documentation |
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.
dixon2002(datos, nsim = 99)
datos |
|
nsim |
number of simulations for the randomization approximation of the p-values. |
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-value can be obtained from the numerical evaluation of the cumulative normal distribution; when the sample size is small, a p-value on the observed counts in each cell (N[ij]) may be obtained by simulation, i.e, by condicting a randomization test.
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.
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. |
pNr |
If nsim !=0, p-values of the observed counts in each cell 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 pNr 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). |
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.
Philip M. Dixon . Marcelino de la Cruz wrote the wrapper code for the ecespa
version.
Dixon, P.M. 2002. Nearest-neighbor contingency table analysis of spatial segregation for several species. Ecoscience, 9 (2): 142-151. doi: 10.1080/11956860.2002.11682700.
K012
for another segregation test, based in the differences of univariate and bivariate K-functions. A faster version of this function, with code implemented in FORTRAN it is available in function dixon
in dixon.
data(swamp) dixon2002(swamp,nsim=99)
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